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Phase diagram and scaling behavior of a PT symmetric non-Hermitian Bose-Hubbard system

L. Jin, Zhida Song

Published May 31, 2011• 0 citations
OpenAlex

Abstract

We study the phase diagram of a PT symmetric non-Hermitian Bose-Hubbard model. Using both analytical and numerical approaches, we find that even small on-site interaction can break the PT symmetry drastically. It has been demonstrated that the scaling law can be established for the exceptional point in small U limit. Based on numerical approach, we also find that the phase diagram shows rich structure for medium U: there exist multiple regions in which the PT symmetry is unbroken.

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We study the phase diagram of a PT symmetric non-Hermitian Bose-Hubbard model. Using both analytical and numerical approaches, we find that even small on-site interaction can break the PT symmetry drastically. It has been demonstrated that the scaling law can be established for the exceptional point in small U limit. Based on numerical approach, we also find that the phase diagram shows rich structure for medium U: there exist multiple regions in which the PT symmetry is unbroken.
We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a Hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, although the exponent is reduced from -1 due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-Hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT symmetry, respectively. Our results challenge the concept of universality in non-Hermitian systems, where quantum criticality can be masked due to non-Hermiticity.
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.
Abstract We study the dynamics of correlations in a paradigmatic setup to observe PT -symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are created, despite the system being driven only incoherently, and can survive indefinitely. Both total and QCs exhibit different scalings of their long-time behavior in the PT -broken/unbroken phase and at the exceptional point (EP). In particular, PT symmetry breaking is accompanied by non-zero stationary QCs. This is analytically shown and quantitatively explained in terms of entropy balance. The EP in particular stands out as the most classical configuration, as classical correlations diverge while QCs vanish.
We study a non-Hermitian PT−PT-PT−symmetric generalization of an NNN-particle, two-mode Bose-Hubbard system, modeling for example a Bose-Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analyzed drawing special attention to the occurrence and unfolding of exceptional points (EPs). We find that for vanishing particle interaction there are only two EPs of order N+1N+1N+1 which under perturbation unfold either into [(N+1)/2][(N+1)/2][(N+1)/2] eigenvalue pairs (and in case of N+1N+1N+1 odd, into an additional zero-eigenvalue) or into eigenvalue triplets (third-order eigenvalue rings) and (N+1)mod  3(N+1)\mod 3(N+1)mod3 single eigenvalues, depending on the direction of the perturbation in parameter space. This behavior is described analytically using perturbational techniques. More general EP unfoldings into eigenvalue rings up to (N+1)(N+1)(N+1)th order are indicated.
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.