We study the connections among particle statistics, frustration, and ground-state energy in quantum many-particle systems. In the absence of interaction, the influence of particle statistics on the ground-state energy is trivial: the ground-state energy of noninteracting bosons is lower than that of free fermions because of Bose-Einstein condensation and Pauli exclusion principle. In the presence of hard-core or other interaction, however, the comparison is not trivial. Nevertheless, the ground-state energy of hard-core bosons is proved to be lower than that of spinless fermions, if all the hopping amplitudes are non-negative. The condition can be understood as the absence of frustration among hoppings. By mapping the many-body Hamiltonian to a tight-binding model on a fictitious lattice, we show that the Fermi statistics of the original particles introduces an effective magnetic flux in the fictitious lattice. The latter can be effectively regarded as a kind of frustration since it leads to a destructive interference among different paths along which a single particle is propagating. If we introduce hopping frustration, the hopping frustration is expected to compete with the effective frustration due to the Fermi statistics, leading to the possibility that the ground-state energy of hard-core bosons can be higher than that of fermions. We present several examples, in which the ground-state energy of hard-core bosons is proved to be higher than that of fermions due to the hopping frustration. The basic ideas were reported in a previous paper [W.-X. Nie, H. Katsura, and M. Oshikawa, Phys. Rev. Lett. 111, 100402 (2013)]; more details and several extensions, including one to the spinful case, are discussed in this paper.We study the connections among particle statistics, frustration, and ground-state energy in quantum many-particle systems. In the absence of interaction, the influence of particle statistics on the ground-state energy is trivial: the ground-state energy of noninteracting bosons is lower than that of free fermions because of Bose-Einstein condensation and Pauli exclusion principle. In the presence of hard-core or other interaction, however, the comparison is not trivial. Nevertheless, the ground-state energy of hard-core bosons is proved to be lower than that of spinless fermions, if all the hopping amplitudes are non-negative. The condition can be understood as the absence of frustration among hoppings. By mapping the many-body Hamiltonian to a tight-binding model on a fictitious lattice, we show that the Fermi statistics of the original particles introduces an effective magnetic flux in the fictitious lattice. The latter can be effectively regarded as a kind of frustration since it leads to a destructive interference among different paths along which a single particle is propagating. If we introduce hopping frustration, the hopping frustration is expected to compete with the effective frustration due to the Fermi statistics, leading to the possibility that the ground-state energy of hard-core bosons can be higher than that of fermions. We present several examples, in which the ground-state energy of hard-core bosons is proved to be higher than that of fermions due to the hopping frustration. The basic ideas were reported in a previous paper [W.-X. Nie, H. Katsura, and M. Oshikawa, Phys. Rev. Lett. 111, 100402 (2013)]; more details and several extensions, including one to the spinful case, are discussed in this paper.

arXiv:1401.2090Physical review. B./Physical review. BMar 30, 20189 citations

One-dimensional hard-core anyons under dephasing

Enguo Guan, Yuzhu Jiang, Xi-Wen Guan

We present a Bethe-ansatz-solvable dissipative model of one-dimensional hard-core anyons under dephasing, where the particles obey fractional statistics. We establish an exact mapping between the Liouvillian and a non-Hermitian Hubbard model with special twisted boundary conditions. With the help of string hypothesis, we rigorously calculate the finite-size corrections and the Liouvillian gap in terms of the statistical parameter, total particle number, lattice size, and dissipation strength. The statistical parameter breaks the $\ensuremath{\eta}$-pairing symmetry of the system, partially lifts out the degeneracy of the spectrum, and contributes to the Liouvillian gap in finite-size corrections. We also derive the general form of the equation of motion for expectation values of the $2w$ -point correlator of hard-core anyons and present a proposal for experimentally measuring the correlation function. Our results shed light on the Liouvillians of exactly solvable dissipative models of anyonic particles that obey the fractional statistics.We present a Bethe-ansatz-solvable dissipative model of one-dimensional hard-core anyons under dephasing, where the particles obey fractional statistics. We establish an exact mapping between the Liouvillian and a non-Hermitian Hubbard model with special twisted boundary conditions. With the help of string hypothesis, we rigorously calculate the finite-size corrections and the Liouvillian gap in terms of the statistical parameter, total particle number, lattice size, and dissipation strength. The statistical parameter breaks the $\ensuremath{\eta}$-pairing symmetry of the system, partially lifts out the degeneracy of the spectrum, and contributes to the Liouvillian gap in finite-size corrections. We also derive the general form of the equation of motion for expectation values of the $2w$-point correlator of hard-core anyons and present a proposal for experimentally measuring the correlation function. Our results shed light on the Liouvillians of exactly solvable dissipative models of anyonic particles that obey the fractional statistics.

Physical Review ANov 19, 20251 citation

Quantum theory and statistical physics

Wesley E. Brittin, Asım Orhan Barut

Gordon and Breach eBooksJan 1, 196823 citations

Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

Xizhou Qin, Yongguan Ke, Xi‐Wen Guan +3 more

We investigate continuous-time quantum walks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara et al., Nature (London) 502, 76 (2013)]. The two interacting particles can undergo independent walking and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with a statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.We investigate continuous-time quantum walks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara et al., Nature (London) 502, 76 (2013)]. The two interacting particles can undergo independent walking and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with a statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.

arXiv:1409.0306Physical Review ADec 1, 201457 citations

2w

-point correlator of hard-core anyons and present a proposal for experimentally measuring the correlation function. Our results shed light on the Liouvillians of exactly solvable dissipative models of anyonic particles that obey the fractional statistics.