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arXiv:2406.07159 · Physical review. B./Physical review. B

Eigenstate plateau transition and equilibration in one-dimensional quantum lattice models

Wei-Han Li, Abbas Ali Saberi

Published Nov 4, 2024• 1 citation
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Abstract

We report a remarkable spectral phenomenon in a generic quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize, leading to plateaus in the interaction energy. Gaps between plateaus can emerge similarly to continuous phase transitions. Our perturbation analysis indicates that, aside from these gaps, the plateau structure of the spectrum remains stable in the thermodynamic limit. The structured spectrum naturally manifests in far-from-equilibrium dynamics, exhibiting multiple stages. Our findings reveal a connection between emergent properties in high-energy states and equilibration dynamics in closed quantum systems, offering insights into the impact of interactions across the entire energy spectrum. These results directly relate to experiments probing equilibration in quantum spin systems and lattice gases. Published by the American Physical Society 2024

DOI
10.1103/physrevb.110.184104

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Quantum droplets-arising from the delicate balance between repulsive and attractive interactions-continue to be of significant interest in the study of ultracold atomic systems. In this work, we revisit the ground-state properties and collective dynamics of one-dimensional quantum droplets. We identify a critical effective particle number, [Formula: see text], at which the superfluid fraction [Formula: see text] exhibits a distinct inflection point, indicating a structural transition in the ground state. For [Formula: see text], the density profile is sharply peaked, whereas for [Formula: see text], it flattens into a plateau-like shape well-approximated by the Thomas-Fermi model. Additionally, we show that super-Gaussian functions provide excellent fits to the ground-state density profiles, offering a simple and accurate modeling approach. To study the system's dynamical behavior, we develop an analytical framework for quantum droplets subjected to a periodic lattice potential. In the weak-lattice limit ([Formula: see text]), the excitation spectrum reveals a Goldstone gapless phonon mode, characteristic of superfluidity. However, at low densities, the inclusion of Lee-Huang-Yang corrections leads to phonon instabilities, consistent with the transition from a peak- to a plateau-like ground state. In the strong-lattice regime (large [Formula: see text]), a gap opens in the lowest excitation modes, suggesting a crossover from a superfluid to a Mott-insulating phase. Our findings should shed light on key aspects of a low-dimensional quantum droplet.
By setting the inverse temperature β loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function Z , if approaching the real β axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the nonunitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between Z and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude, including its scaling behavior at the quantum critical point. We point out Z can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by the numerical tensor renormalization group. We further show that similar patterns of Fisher zeros also emerge in other spin models. Therefore, the approach outlined may serve as a powerful tool for interacting quantum systems. Published by the American Physical Society 2024