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arXiv:2404.17373 · Physical review. B./Physical review. B

Walking behavior induced by PT -symmetry breaking in a non-Hermitian X Y model with clock anisotropy

Eduard Naichuk, Jeroen van den Brink, Flavio S. Nogueira

Published Dec 6, 2024• 2 citations
arXivHTMLPDF

Abstract

A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero-temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental question of how non-Hermiticity affects quantum criticality. In this context, we consider a non-Hermitian system consisting of an X Y model with a complex-valued four-state clock interaction that may or may not have parity-time-reversal ( PT ) symmetry. When the PT symmetry is broken, and time-evolution becomes nonunitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues, but in a highly unconventional way, as the line of fixed points is absent. From the analysis of the d -dimensional renormalization group equations, we obtain that the unconventional behavior in the PT broken regime follows from the collision of two fixed points in the d → 2 limit, leading to walking behavior or pseudocriticality. For d = 2 + 1 the near critical behavior is characterized by a correlation length exponent ν = 3 / 8 , a value smaller than the mean-field one. These results are in sharp contrast with the PT -symmetric case where only one fixed point arises for 2 < d < 4 and in d = 1 + 1 three lines of fixed points occur with a continuously varying critical exponent ν . Published by the American Physical Society 2024

DOI
10.1103/physrevb.110.224505

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A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero-temperature phase transitions that are driven by interactions, just as its Hermitian counterpart, raising the fundamental question of how non-Hermiticity affects quantum criticality. In this context, we consider a non-Hermitian system consisting of an X Y model with a complex-valued four-state clock interaction that may or may not have parity-time-reversal ( PT ) symmetry. When the PT symmetry is broken, and time-evolution becomes nonunitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues, but in a highly unconventional way, as the line of fixed points is absent. From the analysis of the d -dimensional renormalization group equations, we obtain that the unconventional behavior in the PT broken regime follows from the collision of two fixed points in the d → 2 limit, leading to walking behavior or pseudocriticality. For d = 2 + 1 the near critical behavior is characterized by a correlation length exponent ν = 3 / 8 , a value smaller than the mean-field one. These results are in sharp contrast with the PT -symmetric case where only one fixed point arises for 2 < d < 4 and in d = 1 + 1 three lines of fixed points occur with a continuously varying critical exponent ν . Published by the American Physical Society 2024
Abstract Parity Time Reversal (PT) phase transition is a typical characteristic of most of the PT symmetric non-Hermitian (NH) systems. Depending on the theory, a particular system and spacetime dimensionality PT phase transition has various interesting features. In this article we review some of our works on PT phase transitions in quantum mechanics (QM) as well as in Quantum Field theory (QFT). We demonstrate typical characteristics of PT phase transition with the help of several analytically solved examples. In one dimensional QM, we consider examples with exactly as well as quasi exactly solvable (QES) models to capture essential features of PT phase transition. The discrete symmetries have rich structures in higher dimensions which are used to explore the PT phase transition in higher dimensional systems. We consider anisotropic SHOs in two and three dimensions to realize some connection between the symmetry of original hermitian Hamiltonian and the unbroken phase of the NH system. We consider the 2+1 dimensional massless Dirac particle in the external magnetic field with PT symmetric non-Hermitian spin-orbit interaction in the background of the Dirac oscillator potential to show the PT phase transition in a relativistic system. A small mass gap, consistent with the other approaches and experimental observations is generated only in the unbroken phase of the system. Finally we develop the NH formulation in an SU(N) gauge field theoretic model by using the natural but unconventional Hermiticity properties of the ghost fields. Deconfinement to confinement phase transition has been realized as PT phase transition in such a non-hermitian model.
The Berezinskii-Kosterlitz-Thouless (BKT) mechanism governs the critical behavior of a wide range of many-body systems. We show here that this phenomenon is not restricted to conventional many body system but also for the strongly correlated parity-time (PT) symmetry quantum criticality. We show explicitly behaviour of topological excitation for the real and imaginary part of the potential are different through the analysis of second order and third order renormalization group (RG). One of the most interesting feature that we observe from our study the presence of hidden QBKT and also conventional QBKT for the real part of the potential whereas there is no such evidence for the imaginary part of the potential. We also present the exact solution for the RG flow lines. We show explicitly how the physics of single field double frequencies sine-Gordon Hamiltonian effectively transform to the dual field double frequencies sine-Gordon Hamiltonian for a certain regime of parameter space. This is the first example in any quantum many body systems. We present the results of second order and third order RG flow results explicitly for the real and imaginary part of the potential. This PT symmetric system can be experimentally tested in ultra-cold atoms. This work provides a new perspective for the PT symmetric quantum criticality.
Synthetic non-conservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii-Kosterlitz-Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.
One-dimensional non-Hermitian quasicrystals with parity and time-reversal (PT) symmetry can simultaneously exhibit localization-delocalization transition, topological phase transition, and PT-symmetry-breaking transition. This motivates this work to investigate how the absence of PT symmetry impacts topological metal-insulator transitions in non-Hermitian quasicrystals. We propose a non-Hermitian quasiperiodic model that generally does not preserve PT symmetry and demonstrate that, in most parameter regions, such a system supports triple phase transitions that encompass localization, topology, and degeneracy-breaking. The system may also exhibit a particular type of localization-delocalization transition analogous to the Hermitian case, namely, without activating topological phase transitions or degeneracy-breaking transitions. Our work extends the topological metal-insulator transitions previously studied in PT-symmetric systems to a more general class of non-Hermitian setting, and further reveals that non-Hermitian systems can host distinct types of localization behavior.
In recent years, there have been intensive studies of non-Hermitian physics and parity–time (PT) symmetry due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric system is phase transition (spontaneous PT-symmetry breaking), i.e. an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. The generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor. A simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for the realization of non-unitary single-qubit quantum gate. However, studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare. In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. According to these pseudo fixed points, we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although it is non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum, just like the PT symmetric system. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system satisfies fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not meet such a PT symmetry, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the requirement for the PT symmetry.
The occurrence of parity-time reversal (PT)(\mathcal{P}\mathcal{T})(PT) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full real spectrum, which occurs if and only if all the eigenvectors are PT\mathcal{P}\mathcal{T}PT symmetric, can appear only in presence of dimerization, i.e., only if the hopping amplitudes between nearest-neighbor spins assume alternate values along the chain. In order to make a connection between such system and the Hermitian world, we study the critical magnetic properties of the model and look for the conditions that would allow to observe the same phase diagram in the absence of the imaginary field. Such procedure amounts to renormalizing the spin-spin coupling amplitudes.