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Chinese Physics B

P T -symmetry phase transition in a bipartite lattice with long-range interactions

Dapeng 大鹏 Zheng 郑, Siwu Li, Ze-Liang Xiang

Published May 26, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/addcd4

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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 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 study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field approximation for density matrices. The dissipative processes are engineered such that the system, in the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal long-range order. We investigate how the coherent interaction affects the properties of the steady state of the system qualitatively and derive a nonequilibrium phase diagram featuring a phase transition into a steady state without long-range order. The phase diagram also exhibits an extended domain where an instability of the homogeneous steady state gives rise to a persistent density pattern with spontaneously broken translational symmetry. In the limit of low particle density, we provide a precise analytical description of the time evolution during the instability. Moreover, we investigate the transient following a quantum quench of the dissipative processes and we elucidate the prominent role played by collective topological variables in this regime.
Non-Hermitian quantum mechanics with parity-time (PT) symmetry offers a powerful framework for exploring the complex interplay of dissipation and coherent interactions in open quantum systems. While PT-symmetry breaking has been studied in various physical systems, its observation on a quantum many-body level remains elusive. Here, we experimentally realize a non-Hermitian XY model in a strongly-interacting Rydberg-atom array. By measuring the Loschmidt Echo of a fully polarized state, we observe distinct dynamical signatures of a PT-symmetry-breaking phase transition. Dipole interactions are found to play a crucial role, not only determining the transition point but also triggering a non-Hermitian many-body blockade effect that protects the Loschmidt Echo from decay with a non-monotonic dependence on the system size. Our results reveal intricate interaction-induced effects on PT-symmetry breaking and open the door for exploring non-Hermitian many-body dynamics beyond single-particle and mean-field paradigms.
The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.
In this paper, we consider a two-component atomic Bose lattice gas inside an optical cavity to explore a competition between the short-range collisional and cavity-mediated long-range interactions. Utilizing a self-consistent mean-field approach, we map out the ground-state phase diagrams showing the superfluid, lattice supersolid, Mott insulator, and spin-density wave phases. Unlike its single-component analog, this lattice supersolid is here characterized by the coexistence of the superfluid and the spin-density wave. Moreover, for the relatively small long-range interaction, the phase diagrams exhibit a correspondence between the parity of the lattice filling number and the spin imbalance. Finally, we propose how to detect the different quantum phases under current experimental setups.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.