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arXiv:2407.20612 · Physical review. E

Multifractality and excited-state quantum phase transition in ferromagnetic spin-1 Bose-Einstein condensates

Zhen-Xia Niu, Qian Wang

Published Dec 9, 2024• 2 citations
arXivHTMLPDF

Abstract

Multifractality of quantum states plays an important role for understanding numerous complex phenomena observed in different branches of physics. The multifractal properties of the eigenstates allow for characterising various phase transitions. In this work, we perform a thorough analysis of the impacts of an excited-state quantum phase transition (ESQPT) on the fractal behavior of both static and dynamical wave functions in a ferromagentic spin-1 Bose-Einstein condensate. By studying the features of the fractal dimensions, we show how the multifractality of eigenstates and time evolved states are affected by the presence of ESQPT. Specifically, the underlying ESQPT leads to a strong localization effect, which in turn enables us to use it as an indicator of ESQPT. We verify the ability of the fractal dimensions to probe the occurrence of ESQPT through a detailed scaling analysis. We also discuss how the ESQPT manifests itself in the fractal dimensions of the long-time averaged state. Our findings further confirm that the multifractal analysis is a powerful tool for studying of phase transitions in quantum many-body systems and also hint an potential application of ESQPTs in the burgeoning field of state preparation engineering.

DOI
10.1103/physreve.110.064112

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Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-12\frac{1}{2}21​ system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.
Abstract We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. We classify typical ESQPT signatures in the spectra of energy eigenstates with respect to the underlying classical dynamics and outline a variety of quantum systems in which they occur. We describe thermodynamic and dynamic consequences of ESQPTs, like those in microcanonical thermodynamics, quantum quench dynamics, and in the response to nearly adiabatic or periodic driving. We hint at some generalizations of the ESQPT concept in periodic lattices and in resonant tunneling systems.
Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.
The interplay between quantum criticality and ergodicity breaking constitutes a central challenge in complex quantum many-body systems. Here, we investigate ground-state quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), as well as ergodic-nonergodic transition in the cavity Heisenberg spin-chain (CHS) model. By combining quantum information measures with semiclassical fixed-point analysis, we identify a deformed phase that interpolates between the normal and superradiant phases, featuring a logarithmic nonanalyticity in the density of states (DoS) and two additional jump discontinuities. We further elucidate the spectral-structure mechanism underlying the connection between ESQPTs and the ergodic--nonergodic transition (ENET) via level statistics, participation ratios, and multifractal analysis. Our results provide a general framework for characterizing phase structures and spectral features in light--matter quantum many-body systems.