Exact solution of the Bose Hubbard model with unidirectional hopping

• URL: http://arxiv.org/abs/2305.00439v2
• Date: Wed, 28 Feb 2024 03:16:15 GMT
• Title: Exact solution of the Bose Hubbard model with unidirectional hopping
• Authors: Mingchen Zheng, Yi Qiao, Yupeng Wang, Junpeng Cao, Shu Chen
• Abstract summary: A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. We prove the integrability of the model and derive the Bethe ansatz equations. The exact eigenvalue spectrum can be obtained by solving these equations.
• Score: 4.430341888774933
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact eigenvalue spectrum can be obtained by solving these equations. The distribution of Bethe roots reveals the presence of a superfluid-Mott insulator transition at the ground state, and the critical point is determined. By adjusting the boundary parameter, we demonstrate the existence of non-Hermitian skin effect even in the presence of interaction, but it is completely suppressed for the Mott insulator state in the thermodynamical limit. Our result represents a new class of exactly solvable non-Hermitian many-body systems, which have no Hermitian correspondence and can be used as a benchmark for various numerical techniques developed for non-Hermitian many-body systems.

Related papers

• Bardeen-Cooper-Schrieffer interaction as an infinite-range Penson-Kolb pairing mechanism [0.0]
  We show that the well-known $(kuparrow, -kdownarrow)$ Bardeen-Cooper-Schrieffer interaction, when considered in real space, is equivalent to an infinite-range Penson-Kolb pairing mechanism. We investigate the dynamics of fermionic particles confined in a ring-shaped lattice.
  arXiv  Detail & Related papers  (2024-01-30T10:29:46Z)
• Prepotential Approach: a unified approach to exactly, quasi-exactly, and rationally extended solvable quantal systems [0.0]
  We give a brief overview of a simple and unified way, called the prepotential approach. It treats both exact and quasi-exact solvabilities of the one-dimensional Schr"odinger equation. We illustrate the approach by several paradigmatic examples of Hermitian and non-Hermitian Hamiltonians with real energies.
  arXiv  Detail & Related papers  (2023-10-22T11:40:00Z)
• Bethe ansatz solutions and hidden $sl(2)$ algebraic structure for a class of quasi-exactly solvable systems [0.638421840998693]
  We revisit a class of models for which the odd solutions were largely missed previously in the literature. We present a systematic and unified treatment for the odd and even sectors of these models. We also make progress in the analysis of solutions to the Bethe ansatz equations in the spaces of model parameters.
  arXiv  Detail & Related papers  (2023-09-21T02:04:44Z)
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model [0.8258451067861933]
  We show that the effect of a Bosonic environment linearly coupled to a quantum system can be simulated by a Gaussian Lindblad master equation. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure.
  arXiv  Detail & Related papers  (2023-01-18T14:17:17Z)
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance [0.39089069256361736]
  We develop a discrete fermion approach for modelling the strong interaction of an arbitrary system interacting with continuum electronic reservoirs. For a non-interacting single-resonant level, we benchmark our approach against an analytical solution and an exact hierachical-equations-of-motion approach.
  arXiv  Detail & Related papers  (2022-07-12T18:18:53Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results [68.8204255655161]
  We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
  arXiv  Detail & Related papers  (2021-05-11T14:08:02Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model [55.2480439325792]
  We study the nonequilibrium dynamics after an interaction quench in the two-dimensional Hubbard model using the recently introduced fermionic truncated Wigner approximation (fTWA) We show that fTWA is exact at least up to and including the prethermalization dynamics.
  arXiv  Detail & Related papers  (2020-07-09T20:59:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.