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arXiv:2106.15040 · Physical review. B./Physical review. B

Probing the superfluid-insulator phase transition by a non-Hermitian external field

X. Z. Zhang, Z. Song

Published Sep 3, 2021• 8 citations
arXivHTMLPDF

Abstract

We study the response of a thermal state of the Hubbard-like system to either global or local non-Hermitian perturbation, which coalesces the degenerate ground state within the U(1) symmetry breaking phase. We show that the dynamical response of the system is strongly sensitive to the underlying quantum phase transition (QPT) from a Mott insulator to a superfluid state. The Uhlmann fidelity in the superfluid phase decays to a steady value determined by the order of the exceptional point (EP) within the subspace spanned by the degenerate ground states, but remains almost unchanged in the Mott insulating phase. It demonstrates that the phase diagram at zero temperature is preserved even though a local probing field is applied. Specifically, two celebrated models, including the Bose-Hubbard model and the Jaynes-Cummings-Hubbard model, are employed to demonstrate this property in the finite-size system, wherein fluctuations of the boson and polariton number are observed based on EP dynamics. This work presents an alternative approach to probe the superfluid-insulator QPT at nonzero temperature.

DOI
10.1103/physrevb.104.094301

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We study the response of a thermal state of the Hubbard-like system to either global or local non-Hermitian perturbation, which coalesces the degenerate ground state within the U(1) symmetry breaking phase. We show that the dynamical response of the system is strongly sensitive to the underlying quantum phase transition (QPT) from a Mott insulator to a superfluid state. The Uhlmann fidelity in the superfluid phase decays to a steady value determined by the order of the exceptional point (EP) within the subspace spanned by the degenerate ground states, but remains almost unchanged in the Mott insulating phase. It demonstrates that the phase diagram at zero temperature is preserved even though a local probing field is applied. Specifically, two celebrated models, including the Bose-Hubbard model and the Jaynes-Cummings-Hubbard model, are employed to demonstrate this property in the finite-size system, wherein fluctuations of the boson and polariton number are observed based on EP dynamics. This work presents an alternative approach to probe the superfluid-insulator QPT at nonzero temperature.
We study the response of a thermal state of an Ising chain to a nonlocal non-Hermitian perturbation, which coalesces the topological Kramer-like degeneracy in the ferromagnetic phase. The dynamic responses for initial thermal states in different quantum phases are distinct. The final state always approaches its half component with a fixed parity in the ferromagnetic phase but remains almost unchanged in the paramagnetic phase. This indicates that the phase diagram at zero temperature is completely preserved at finite temperatures. Numerical simulations for Loschmidt echoes demonstrate such dynamical behaviors in finite-size systems. In addition, it provides a clear manifestation of the bulk-boundary correspondence at nonzero temperatures. This work presents an alternative approach to understanding the quantum phase transitions of quantum spin systems at nonzero temperatures.
We study the zero temperature mean-field phase diagram of the Bose-Hubbard model in the presence of local coupling between the bosons and an external bath. We consider a coupling that conserves the on-site occupation number, preserving the robustness of the Mott-insulator and superfluid phases. We show that the coupling to the bath renormalizes the chemical potential and the interaction between the bosons and reduces the size of the superfluid regions between the insulating lobes. For strong enough coupling, a finite value of hopping is required to obtain superfluidity around the degeneracy points where Mott-insulator phases with different occupation numbers coexist.
The quantum phase transition between Mott insulator and superfluid is studied in the two-dimensional Jaynes-Cummings square lattice in which the counter-rotating coupling (CRC) is included. Both the ground state and the spectra of low-lying excitations are obtained with use of a sophisticated unitary transformation. This CRC is shown not only to induce a long-range interaction between cavities, favoring the long-range superfluid order, but also to break the conservation of local polariton number at each site, leading to the absence of the Mott lobes in the phase diagram, in sharp contrast with the case without the CRC as well as that of the Bose-Hubbard model.
We investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.
We investigated the behavior of non-Hermitian bosonic gases with Hubbard interactions in one-dimensional (1D) zigzag optical lattices through the calculation of dynamic response functions. Our findings showed the existence of a non-Hermitian quantum phase transition that is dependent on the pseudo-Hermitian symmetry. The system tends to exhibit a superfluid phase when subjected to weak dissipation. While under strong dissipation, the pseudo-Hermitian symmetry of the system is partially broken, leading to a transition toward a normal liquid phase. As the dissipation increases beyond the critical threshold, the pseudo-Hermitian symmetry is completely broken, resulting in a Mott-insulator phase. We propose an experimental setup using 1D zigzag optical lattices containing two-electron atoms to realize this system. In this paper, we emphasize the key role of non-Hermiticity in quantum phase transitions and offer a theoretical framework as well as experimental methods for understanding the behavior of dissipative quantum systems, implicating significant development of quantum devices and technologies.
We develop a unified field-theoretical description of the Bose-Hubbard model that captures low-energy dynamics across the insulator-to-superfluid transition. We show that commonly used cumulant expansions about the Mott ground state fail in the superfluid phase not only quantitatively but also fundamentally, because they impose an incorrect canonical structure. Expanding instead about the appropriate mean-field saddle point, we derive an effective action in which the dynamics of fluctuations are governed by a Berry-phase term, giving rise to an emergent magnetic field in the associated oscillator description. This field encodes particle-hole symmetry breaking in both the Mott-insulator phase and the superfluid, and vanishes at the point where a pure Goldstone mode emerges. The resulting effective hydrodynamic theory admits a speed of sound that approaches the Bogoliubov limit in the weakly interacting regime, demonstrating consistency across the entire phase diagram, from the Mott-insulator to the deep superfluid regime. While the total density remains continuous within mean-field theory, we find that quantum fluctuations generate a discontinuous contribution at the quantum phase transition, which vanishes at the tip of the Mott lobe.