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arXiv:2003.08864 · Physical Review A

Interaction-induced dynamical PT -symmetry breaking in dissipative Fermi-Hubbard models

Lei Pan, Xueliang Wang, Xiaoling Cui, Shu Chen

Published Aug 6, 2020• 29 citations
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Abstract

We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time ($\mathcal{PT}$) symmetry if we compensate the system additionally with an overall gain term. By solving exactly the two-site Lindblad equation with fixed dissipation, we find that the dynamics of the rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in the scheme of non-Hermitian effective Hamiltonians. This instability is also observed in multisite systems and closely related to the $\mathcal{PT}$-symmetry breaking accompanied by appearance of complex eigenvalues of the effective Hamiltonian. Moreover, we unveil that the dynamical instability of the antiferromagnetic Mott phase comes from the $\mathcal{PT}$-symmetry breaking in highly excited bands, although the low-energy effective model of the non-Hermitian Hubbard model in the strongly interacting regime is always Hermitian. We also provide a quantitative estimation of the time for the observation of dynamical $\mathcal{PT}$-symmetry breaking which could be probed in experiments.

DOI
10.1103/physreva.102.023306

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PT{\mathcal{P}}{\mathcal{T}}PT-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain
Abstract Nonequilibrium phase transitions in open dissipative systems can be described as instabilities in the spectra and wavefunctions of effective non-Hermitian Hamiltonians invariant under simultaneous parity ( P\boldsymbol{\mathcal{P}}P P ) and time-reversal ( T\boldsymbol{\mathcal{T}}T T ) transformations. The degree of non-Hermiticity reflects the strength of the external drive and dissipation, and the transition is described as a loss of the PT\boldsymbol{\mathcal{P}}\boldsymbol{\mathcal{T}}PT PT symmetry of the solutions corresponding to stationary low-drive dynamics. This approach has been successfully applied to spin, superconducting, and Mott insulator systems. However, the microscopic foundations for the employed phenomenological models are currently lacking. Here we propose a microscopic mechanism leading to the PT\boldsymbol{\mathcal{P}}\boldsymbol{\mathcal{T}}PT PT -symmetric effective model in the context of the nonequilibrium Mott transition in a dissipative Hubbard chain. Our model comprises a half-filled fermionic Hubbard chain subject to a constant electric field. The dissipation is introduced via the electron-phonon coupling. We obtain the explicit expressions for the non-Hermitian parameter in terms of the electron-phonon coupling strength and driving field. Analyzing the implications of microscopic model, we find a re-entrant Mott insulator with the increasing electric field for phonon density of states that increases slower than the square of the energy (such as in one or two dimensions), or varies non-monotonously with energy.
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We describe the critical behavior of the electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P)(\mathcal{P})(P) and time-reversal (T)(\mathcal{T})(T) operations. The dynamic Mott transition is identified as a PT\mathcal{PT}PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT\mathcal{PT}PT symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive the renormalization and collapse of the Mott gap at the dielectric breakdown and describe the resulting critical behavior of transport characteristics. The obtained critical exponent is in an excellent agreement with experimental findings.
We study the PT\mathcal{PT}PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact PT\mathcal{PT}PT-symmetric phase to the phase with spontaneously breaking PT\mathcal{PT}PT symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and determine the exceptional point for the symmetry breaking analytically. In the PT\mathcal{PT}PT-symmetry-breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian PT\mathcal{PT}PT-symmetric potentials.
We study an imaginary Stark ladder model, and we propose a realization of the model in a dissipative chain with linearly increasing site-dependent dissipation strength. Due to the existence of KKK symmetry and passive PT\mathcal{PT}PT symmetry, the model exhibits quite a different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive PT\mathcal{PT}PT-symmetry breaking transition, with the shifted eigenvalues changing from real to complex, and then a KKK-symmetry restoring transition, characterized by the emergence of a pure imaginary spectrum with equal spacing. Accordingly, the eigenstates change from PT\mathcal{PT}PT-unbroken extended states to PT\mathcal{PT}PT-broken states, and finally to Stark-localized states. In the framework of the quantum open system governed by the Lindblad equation with linearly increasing site-dependent dissipation, we unveil that the dynamical evolution of a single-particle correlation function is governed by the Hamiltonian of the imaginary Stark ladder model. By studying the dynamical evolution of the density distribution under various initial states, we demonstrate that the damping dynamics displays distinct behaviors in different regions. A localized damping is observed in the strong dissipation limit.