Temperature effect on a kicked Tonks-Girardeau gas

TL;DR

This work addresses how finite temperature affects many-body dynamical localization (MBDL) and the localization–delocalization transition in a kicked Tonks-Girardeau gas under periodic and quasiperiodic drives. Using a grand-canonical lattice approach and Jordan–Wigner mapping to noninteracting fermions, the authors extract observables from the equal-time OPDM and demonstrate that MBDL persists at finite temperatures, with increased localization length and degraded coherence, accompanied by effective thermalization described by an emergent $T_{\mathrm{eff}}$ and $\mu_{\mathrm{eff}}$. In the quasiperiodic case, they reveal an intermediate-temperature MBDL transition and establish one-parameter scaling laws for momentum distributions in localized, critical, and delocalized phases, along with a consistent large-$k$ tail governed by Tan's contact. The results provide practical guidance for cold-atom experiments at finite temperature and expand the understanding of dynamical localization phenomena beyond zero temperature.

Abstract

It is widely recognized that finite temperatures degrade quantum coherence and can induce thermalization. Here, we study the effect of finite temperature on a kicked Tonks--Girardeau gas, which is known to exhibit many--body dynamical localization and delocalization under periodic and quasiperiodic kicks, respectively. We find that many--body dynamical localization persists at finite--and even high--temperatures, although the coherence of the localized state is further degraded. In particular, we demonstrate a modified effective thermalization of the localized state by considering the initial temperature. Moreover, we show many--body dynamical localization transition at intermediate temperature. Our work extends the study of many--body dynamical localization and delocalization to the finite--temperature regime, providing comprehensive guidance for cold--atom experiments.

Figures (9)

• Figure 1: (a) The kinetic energy dynamics of the periodically kicked Tonks gas for different initial temperature $T_0$. (b-d) The corresponding fermionic momentum distribution (b), the bosonic momentum distribution (c), and the bosonic correlation function (d) for different initial temperature $T_0$. The dashed lines (blue and red) denote the initial state at $t=0$ while the solid lines denote the final state at $t=500$. The particle number, anisotropy, kick strength and effective Planck constant are respectively $N=31, \varepsilon=0, K=4, \hbar_{\mathrm{eff}}=1$.
• Figure 2: Time evolution of the extracted effective temperature $T_{\mathrm{eff}}$ (a) and effective chemical potential $\mu_{\mathrm{eff}}$ (b) for different initial temperature $T_0$. The particle number, anisotropy, kick strength and effective Planck constant are respectively $N=31, \varepsilon=0, K=4, \hbar_{\mathrm{eff}}=1$.
• Figure 3: The bosonic momentum distribution at $t=500$ for different initial temperature $T_0$ in a log-log scale. The dashed lines denote the predicted algebraic decay $n^{\mathrm{B}}(k)\propto \mathcal{C}_{th}/k^{4}$ with $\mathcal{C}_{th}$ being the Tan's contact of a thermal Tonks gas. All the data have been shifted for better visibility. Inset shows the same data in a linear scale. The particle number, anisotropy, kick strength and effective Planck constant are respectively $N=31, \varepsilon=0, K=4, \hbar_{\mathrm{eff}}=1$.
• Figure 4: (a) $p_{\mathrm{loc}}/p_{\mathrm{F}}$ as a function of $T_{\mathrm{eff}}/\varepsilon_{\mathrm{F}}$ at $t=500$ for different particle numbers $N$ and different initial temperature $T_0$. The solid (dashed) lines denote the corresponding prediction for low (high) temperature. (b) $r_{\mathrm{c}}p_{\mathrm{F}}/\hbar_{\mathrm{eff}}$ as a function of $\varepsilon_{\mathrm{F}}/T_{\mathrm{eff}}$ at $t=500$ for different particle numbers $N$ and different initial temperature $T_0$. The black solid and dashed lines show the predictions for $\mu_{\mathrm{eff}}/T_{\mathrm{eff}}\gg 1$ and $\mu_{\mathrm{eff}}/T_{\mathrm{eff}}\ll 1$, respectively. The anisotropy, kick strength and effective Planck constant are respectively $\varepsilon=0, K=4, \hbar_{\mathrm{eff}}=1$.
• Figure 5: The extracted dynamical exponent $\gamma$ as a function of the anisotropy $\varepsilon$ and the kick strength $K$. The blue (red) regime denotes the localized (delocalized) phase, while the white regime denotes the anomalous diffusion with $\gamma\approx2/3$. The data are computed from the single-particle quasiperiodic QKR at $T_0=0.55\varepsilon_{\mathrm{F}}$. The particle number, and the effective Planck constant are respectively $N=1, \hbar_{\mathrm{eff}}=2.89$.