The Approximation of Bosonic System by Fermion in Quantum Cellular Automaton

In one-dimensional multiparticle Quantum Cellular Automaton (QCA), the approximation of the bosonic system by fermion (boson-fermion correspondence) can be derived in a rather simple and intriguing way, where the principle to impose zero-derivative boundary conditions of one-particle QCA is also analogously used in particle-exchange boundary conditions. As a clear cut demonstration of this approximation, we calculate the ground state of few-particle systems in a box using imaginary time evolution simulation in 2nd quantization form as well as in 1st quantization form. Moreover in this 2nd quantized form of QCA calculation, we use Time Evolving Block Decimation (TEBD) algorithm. We present this demonstration to emphasize that the TEBD is most natu-rally regarded as an approximation method to the 2nd quantized form of QCA.