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Pseudo-fermion functional renormalization group for spin models. 自旋模型的伪费米子函数重正化群
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2024-02-15 DOI: 10.1088/1361-6633/ad208c
Tobias Müller, Dominik Kiese, Nils Niggemann, Björn Sbierski, Johannes Reuther, Simon Trebst, Ronny Thomale, Yasir Iqbal
{"title":"Pseudo-fermion functional renormalization group for spin models.","authors":"Tobias Müller, Dominik Kiese, Nils Niggemann, Björn Sbierski, Johannes Reuther, Simon Trebst, Ronny Thomale, Yasir Iqbal","doi":"10.1088/1361-6633/ad208c","DOIUrl":"10.1088/1361-6633/ad208c","url":null,"abstract":"<p><p>For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of<i>m</i>-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139503308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From caged compounds with isolated U atoms to frustrated magnets with 2- or 3-atom clusters: a review of Al-rich uranium aluminides with transition metals. 从具有孤立铀原子的笼状化合物到具有 2 或 3 原子团簇的受挫磁体:富铝铀铝化物与过渡金属的综述。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2024-02-06 DOI: 10.1088/1361-6633/ad218d
Mathieu Pasturel, Adam Pikul
{"title":"From caged compounds with isolated U atoms to frustrated magnets with 2- or 3-atom clusters: a review of Al-rich uranium aluminides with transition metals.","authors":"Mathieu Pasturel, Adam Pikul","doi":"10.1088/1361-6633/ad218d","DOIUrl":"10.1088/1361-6633/ad218d","url":null,"abstract":"<p><p>Crystal structures and physical properties of four families of Al-rich ternary uranium compounds with transition metals (<i>TE</i>) are reviewed, namely U<i>TE</i><sub>2</sub>Al<sub>20</sub>, U<i>TE</i><sub>2</sub>Al<sub>10</sub>, U<sub>6</sub><i>TE</i><sub>4</sub>Al<sub>43</sub>, and U<sub>3</sub><i>TE</i><sub>4</sub>Al<sub>12</sub>. The compounds can be described as consisting of 1 (isolated), 2 (dumbbells) or 3 (triangles) uranium atom clusters, surrounded (1-2-20, 1-2-10 and 6-4-43) or not (3-4-12) by large cages, which strongly influence their magnetic and related properties. Indeed, the ground states of the described systems evolve from Curie-like paramagnetism in the case of the phases with well-isolated, single U-atoms, to complex magnetic order or possible frustrated magnetism in the case of the systems with uranium triangles forming a breathing kagome lattice. We argue that the four families of uranium aluminides described in this review provide a unique opportunity to study magnetic interactions between U magnetic moments while gradually increasing the number of their nearest magnetic neighbors, and may also be helpful in understanding the fundamental origin of magnetic freezing phenomena.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139543470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Molecular nanomagnets: a viable path toward quantum information processing? 分子纳米磁体:通向量子信息处理的可行之路?
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2024-02-05 DOI: 10.1088/1361-6633/ad1f81
A Chiesa, P Santini, E Garlatti, F Luis, S Carretta
{"title":"Molecular nanomagnets: a viable path toward quantum information processing?","authors":"A Chiesa, P Santini, E Garlatti, F Luis, S Carretta","doi":"10.1088/1361-6633/ad1f81","DOIUrl":"https://doi.org/10.1088/1361-6633/ad1f81","url":null,"abstract":"<p><p>Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":"87 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139682119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Beyond Kitaev physics in strong spin-orbit coupled magnets. 强自旋轨道耦合磁体中的基塔耶夫物理学。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2024-02-02 DOI: 10.1088/1361-6633/ad208d
Ioannis Rousochatzakis, Natalia B Perkins, Qiang Luo, Hae-Young Kee
{"title":"Beyond Kitaev physics in strong spin-orbit coupled magnets.","authors":"Ioannis Rousochatzakis, Natalia B Perkins, Qiang Luo, Hae-Young Kee","doi":"10.1088/1361-6633/ad208d","DOIUrl":"10.1088/1361-6633/ad208d","url":null,"abstract":"<p><p>We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139503307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding. 低维系统中电荷密度波的结构方法:电子不稳定性与化学键
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2024-01-30 DOI: 10.1088/1361-6633/ad124f
Jean-Paul Pouget, Enric Canadell
{"title":"Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding.","authors":"Jean-Paul Pouget, Enric Canadell","doi":"10.1088/1361-6633/ad124f","DOIUrl":"10.1088/1361-6633/ad124f","url":null,"abstract":"<p><p>The charge density wave (CDW) instability, usually occurring in low-dimensional metals, has been a topic of interest for longtime. However, some very fundamental aspects of the mechanism remain unclear. Recently, a plethora of new CDW materials, a substantial fraction of which is two-dimensional or even three-dimensional, has been prepared and characterised as bulk and/or single-layers. As a result, the need for revisiting the primary mechanism of the instability, based on the electron-hole instability established more than 50 years ago for quasi-one-dimensional (quasi-1D) conductors, has clearly emerged. In this work, we consider a large number of CDW materials to revisit the main concepts used in understanding the CDW instability, and emphasise the key role of the momentum dependent electron-phonon coupling in linking electronic and structural degrees of freedom. We argue that for quasi-1D systems, earlier weak coupling theories work appropriately and the energy gain due to the CDW and the concomitant periodic lattice distortion (PLD) remains primarily due to a Fermi surface nesting mechanism. However, for materials with higher dimensionality, intermediate and strong coupling regimes are generally at work and the modification of the chemical bonding network by the PLD is at the heart of the instability. We emphasise the need for a microscopic approach blending condensed matter physics concepts and state-of-the-art first-principles calculations with quite fundamental chemical bonding ideas in understanding the CDW phenomenon in these materials.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138489314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum phase transitions in two-dimensional superconductors: a review on recent experimental progress. 二维超导体中的量子相变:近期实验进展综述。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2023-12-29 DOI: 10.1088/1361-6633/ad14f3
Ziqiao Wang, Yi Liu, Chengcheng Ji, Jian Wang
{"title":"Quantum phase transitions in two-dimensional superconductors: a review on recent experimental progress.","authors":"Ziqiao Wang, Yi Liu, Chengcheng Ji, Jian Wang","doi":"10.1088/1361-6633/ad14f3","DOIUrl":"10.1088/1361-6633/ad14f3","url":null,"abstract":"<p><p>Superconductor-insulator/metal transition (SMT) as a paradigm of quantum phase transition has been a research highlight over the last three decades. Benefit from recent developments in the fabrication and measurements of two-dimensional (2D) superconducting films and nanodevices, unprecedented quantum phenomena have been revealed in the quantum phase transitions of 2D superconductors. In this review, we introduce the recent progress on quantum phase transitions in 2D superconductors, focusing on the quantum Griffiths singularity (QGS) and anomalous metal state. Characterized by a divergent critical exponent when approaching zero temperature, QGS of SMT is discovered in ultrathin crystalline Ga films and subsequently detected in various 2D superconductors. The universality of QGS indicates the profound influence of quenched disorder on quantum phase transitions. Besides, in a 2D superconducting system, whether a metallic ground state can exist is a long-sought mystery. Early experimental studies indicate an intermediate metallic state in the quantum phase transition of 2D superconductors. Recently, in high-temperature superconducting films with patterned nanopores, a robust anomalous metal state (i.e. quantum metal or Bose metal) has been detected, featured as the saturated resistance in the low temperature regime. Moreover, the charge-2<i>e</i>quantum oscillations are observed in nanopatterned films, indicating the bosonic nature of the anomalous metal state and ending the debate on whether bosons can exist as a metal. The evidences of the anomalous metal states have also been reported in crystalline epitaxial thin films and exfoliated nanoflakes, as well as granular composite films. High quality filters are used in these works to exclude the influence of external high frequency noises in ultralow temperature measurements. The observations of QGS and metallic ground states in 2D superconductors not only reveal the prominent role of quantum fluctuations and dissipations but also provide new perspective to explore quantum phase transitions in superconducting systems.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138814780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum systems in silicon carbide for sensing applications. 用于传感应用的碳化硅量子系统。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2023-12-20 DOI: 10.1088/1361-6633/ad10b3
S Castelletto, C T-K Lew, Wu-Xi Lin, Jin-Shi Xu
{"title":"Quantum systems in silicon carbide for sensing applications.","authors":"S Castelletto, C T-K Lew, Wu-Xi Lin, Jin-Shi Xu","doi":"10.1088/1361-6633/ad10b3","DOIUrl":"10.1088/1361-6633/ad10b3","url":null,"abstract":"<p><p>This paper summarizes recent studies identifying key qubit systems in silicon carbide (SiC) for quantum sensing of magnetic, electric fields, and temperature at the nano and microscale. The properties of colour centres in SiC, that can be used for quantum sensing, are reviewed with a focus on paramagnetic colour centres and their spin Hamiltonians describing Zeeman splitting, Stark effect, and hyperfine interactions. These properties are then mapped onto various methods for their initialization, control, and read-out. We then summarised methods used for a spin and charge state control in various colour centres in SiC. These properties and methods are then described in the context of quantum sensing applications in magnetometry, thermometry, and electrometry. Current state-of-the art sensitivities are compiled and approaches to enhance the sensitivity are proposed. The large variety of methods for control and read-out, combined with the ability to scale this material in integrated photonics chips operating in harsh environments, places SiC at the forefront of future quantum sensing technology based on semiconductors.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138464956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors. 铁基超导体的大规模、有序和可调谐马约拉纳零模晶格。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2023-11-28 DOI: 10.1088/1361-6633/ad0c5c
Geng Li, Meng Li, Xingtai Zhou, Hong-Jun Gao
{"title":"Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors.","authors":"Geng Li, Meng Li, Xingtai Zhou, Hong-Jun Gao","doi":"10.1088/1361-6633/ad0c5c","DOIUrl":"10.1088/1361-6633/ad0c5c","url":null,"abstract":"<p><p>Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS<sub>2</sub>. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe<sub>0.55</sub>Se<sub>0.45</sub>and (Li<sub>0.84</sub>Fe<sub>0.16</sub>)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"107593064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update. 应变石墨烯和其他应变单层和多层的机械、电子、光学、压电和铁电性能:更新。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2023-11-28 DOI: 10.1088/1361-6633/ad06db
Gerardo G Naumis, Saúl A Herrera, Shiva P Poudel, Hiro Nakamura, Salvador Barraza-Lopez
{"title":"Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update.","authors":"Gerardo G Naumis, Saúl A Herrera, Shiva P Poudel, Hiro Nakamura, Salvador Barraza-Lopez","doi":"10.1088/1361-6633/ad06db","DOIUrl":"10.1088/1361-6633/ad06db","url":null,"abstract":"<p><p>This is an update of a previous review (Naumis<i>et al</i>2017<i>Rep. Prog. Phys.</i><b>80</b>096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (<b>P</b>) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisation<b>P</b>on hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (<i>σ</i>), electric (<b>P</b>) and magnetic (<b>M</b>) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI<sub>2</sub>. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.</p>","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50164035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PT-symmetric, non-Hermitian quantum many-body physics-a methodological perspective. $mathcal{PT}$对称、非埃尔米特量子多体物理——一种方法论视角。
Reports on progress in physics. Physical Society (Great Britain) Pub Date : 2023-11-16 DOI: 10.1088/1361-6633/ad05f3
V Meden, L Grunwald, D M Kennes
{"title":"PT-symmetric, non-Hermitian quantum many-body physics-a methodological perspective.","authors":"V Meden, L Grunwald, D M Kennes","doi":"10.1088/1361-6633/ad05f3","DOIUrl":"10.1088/1361-6633/ad05f3","url":null,"abstract":"<p><p>We review the methodology to theoretically treat parity-time- (PT-) symmetric, non-Hermitian quantum many-body systems. They are realized as open quantum systems withPTsymmetry and couplings to the environment which are compatible.PT-symmetric non-Hermitian quantum systems show a variety of fascinating properties which single them out among generic open systems. The study of the latter has a long history in quantum theory. These studies are based on the Hermiticity of the combined system-reservoir setup and were developed by the atomic, molecular, and optical physics as well as the condensed matter physics communities. The interest of the mathematical physics community inPT-symmetric, non-Hermitian systems led to a new perspective and the development of the elegant mathematical formalisms ofPT-symmetric and biorthogonal quantum mechanics, which do not make any reference to the environment. In the mathematical physics research, the focus is mainly on the remarkable spectral properties of the Hamiltonians and the characteristics of the corresponding single-particle eigenstates. Despite being non-Hermitian, the Hamiltonians can show parameter regimes, in which all eigenvalues are real. To investigate emergent quantum many-body phenomena in condensed matter physics and to make contact to experiments one, however, needs to study expectation values of observables and correlation functions. One furthermore, has to investigate statistical ensembles and not only eigenstates. The adoption of the concepts ofPT-symmetric and biorthogonal quantum mechanics by parts of the condensed matter community led to a controversial status of the methodology. There is no consensus on fundamental issues, such as, what a proper observable is, how expectation values are supposed to be computed, and what adequate equilibrium statistical ensembles and their corresponding density matrices are. With the technological progress in engineering and controlling open quantum many-body systems it is high time to reconcile the Hermitian with thePT-symmetric and biorthogonal perspectives. We comprehensively review the different approaches, including the overreaching idea of pseudo-Hermiticity. To motivate the Hermitian perspective, which we propagate here, we mainly focus on the ancilla approach. It allows to embed a non-Hermitian system into a larger, Hermitian one. In contrast to other techniques, e.g. master equations, it does not rely on any approximations. We discuss the peculiarities ofPT-symmetric and biorthogonal quantum mechanics. In these, what is considered to be an observable depends on the Hamiltonian or the selected (biorthonormal) basis. Crucially in addition, what is denoted as an 'expectation value' lacks a direct probabilistic interpretation, and what is viewed as the canonical density matrix is non-stationary and non-Hermitian. Furthermore, the non-unitarity of the time evolution is hidden within the formalism. We pick up several model Hamiltonians, which so far","PeriodicalId":74666,"journal":{"name":"Reports on progress in physics. Physical Society (Great Britain)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49694856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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