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arXiv:2211.08707 · Physical review. B./Physical review. B

PT -symmetry phase transition in a Bose-Hubbard model with localized gain and loss

Cătălin Paşcu Moca, Doru Sticlet, Balázs Dóra, Gergely Zaránd

Published Mar 6, 2023• 3 citations
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Abstract

We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the $\mathcal{P}\mathcal{T}$ symmetry under some specific conditions and features a $\mathcal{P}\mathcal{T}$-symmetry phase transition. It is characterized by an order parameter corresponding to the population imbalance between even and odd sites,similar to the continuous phase transitions in the Hermitian realm. In the noninteracting limit, we solve the problem exactly and compute the parameter dependence of the order parameter. The interacting limit is addressed at the mean-field level, which allows us to construct the phase diagram for the model. We find that both the interaction and dissipation rates induce $\mathcal{PT}$-symmetry breaking. On the other hand, periodic modulation of the dissipative coupling in time stabilizes the $\mathcal{PT}$-symmetric regime. Our findings are corroborated numerically on a tight-binding chain with gain and loss.

DOI
10.1103/physrevb.107.115111

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We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the PT\mathcal{P}\mathcal{T}PT symmetry under some specific conditions and features a PT\mathcal{P}\mathcal{T}PT-symmetry phase transition. It is characterized by an order parameter corresponding to the population imbalance between even and odd sites,similar to the continuous phase transitions in the Hermitian realm. In the noninteracting limit, we solve the problem exactly and compute the parameter dependence of the order parameter. The interacting limit is addressed at the mean-field level, which allows us to construct the phase diagram for the model. We find that both the interaction and dissipation rates induce PT\mathcal{PT}PT-symmetry breaking. On the other hand, periodic modulation of the dissipative coupling in time stabilizes the PT\mathcal{PT}PT-symmetric regime. Our findings are corroborated numerically on a tight-binding chain with gain and loss.
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 (PT\mathcal{PT}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 PT\mathcal{PT}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 PT\mathcal{PT}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 PT\mathcal{PT}PT-symmetry breaking which could be probed in experiments.
Abstract We investigate the parity–time ( P T ) symmetry-breaking quantum phase transition in a one-dimensional (1D) bosonic lattice featuring cavity-mediated long-range interactions and spatially staggered dissipation. By mapping the system to an effective spin chain under the constraints of hard-core bosons and integrating the mean-field decoupling approach with biorthogonal basis formalism, we derive a self-consistency equation. Numerical simulation results validate that the derived equation quantitatively captures the P T -symmetry order parameter’s phase diagram. Our findings reveal that coherent hopping maintains P T symmetry through quantum fluctuations. Conversely, cavity-engineered long-range interactions, in synergy with staggered dissipation, act in opposition to drive symmetry breaking. This competitive interplay can inspire further exploration of tunable quantum phase transitions in non-Hermitian systems.
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 the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing non-unitary dynamic properties. The interplay of interactions and non-hermiticity results in insulating behavior with a phase diagram divided into three distinct regions, exhibiting either topologically gapped or (real) gapless regimes and a trivial phase. The latter is mapped by the emergence of a local order parameter associated with a charge density wave. A PT{\cal PT}PT-symmetry breaking at the low-lying spectrum occurs when increasing the gain-loss magnitude at a fixed interaction strength, marking the transition from gapped to gapless topological behavior. Further increase leads to the onset of charge ordering in a first-order phase transition in which level crossing takes place in the spectrum's imaginary part. The support that the staggered gain and loss display to robust charge density wave in equilibrium is confirmed in the real-time dynamics in the presence of non-hermiticity, suggesting that engineered gain and loss can be used to tailor an ordered many-body state in experiments.
Parity-time (PT)(\mathcal{PT})(PT) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a PT\mathcal{PT}PT-symmetric Hamiltonian change from real to complex conjugates at a critical value of gain-loss strength that is called the PT\mathcal{PT}PT breaking threshold. Here, we obtain the PT\mathcal{PT}PT threshold for a one-dimensional, finite Kitaev chain---a prototype for a ppp-wave superconductor---in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, on-site potential, and the distance between the gain and loss sites. In addition to a robust, nonlocal threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band structure of the Hermitian Kitaev model. In particular, for an even chain with zero on-site potential, we find a re-entrant PT\mathcal{PT}PT-symmetric phase bounded by second-order EP contours. Our numerical results are supplemented by analytical calculations for small system sizes.