Super-Tonks-Girardeau Quench in the Extended Bose-Hubbard Model

TL;DR

The paper investigates a super-Tonks-Girardeau quench in a one-dimensional extended Bose-Hubbard model with on-site and nearest-neighbor interactions. By combining exact two-body solutions, few-body ED/DMRG/TDVP numerics, and a local-density-approximation framework for macroscopic systems, it maps how a sudden switch from strong repulsion to strong attraction affects post-quench dynamics across gas, liquid, and self-bound Mott insulator phases. The authors identify three regimes—scattering-ground stability, weakly self-bound evaporation, and bound-ground stability with a near-identical superpartner in the attractive sector—controlled by the nearest-neighbor coupling $V$ and its critical values $V_c^{ m olinebreak }^{ m olinebreak 2}$ (with $V_c^{ m } \u2261 -2J$ and corrections of order $J^2/|U|$). A key finding is that a liquid-like state can evaporate after the quench despite attractive interactions, due to enhanced sTG correlations and superexchange effects, providing a diagnostic handle on the phase diagram relevant to current experiments. These results extend sTG physics to lattice systems with nonlocal interactions and offer a practical framework for interpreting non-equilibrium dynamics in the extended Bose-Hubbard context.

Abstract

We investigate the effect of a quench from a one-dimensional gas with strong and repulsive local interactions to a strongly attractive one, known as the super-Tonks-Girardeau effect. By incorporating both an optical lattice and non-local interactions (specifically nearest-neighbor), we discover a previously unexplored phenomenon: the disruption of the state during the quench, but within a specific range of interactions. Our study employs the extended Bose-Hubbard model across various system sizes, starting with analytical results for two atoms and progressing to few-body systems using exact diagonalization, DMRG and TDVP methods. Finally, we use a numerical implementation of the local density approximation for a macroscopic number of atoms. Consistently, our findings unveil a region where the initially self-bound structure expands due to the super-Tonks-Girardeau quench. The fast evaporation provides a tool to characterize the phase diagram in state-of-art experiments exploring the physics of the extended Bose-Hubbard model.

Figures (9)

• Figure 1: Super-Tonks-Girardeau quench dynamics for the phases of the eBH model: gas and the deeply-self-bound Mott insulator phases are stable, while the liquid droplets expand and eventually evaporate.
• Figure 2: The upper panels show the $K=0$ energy spectrum of the eBH model \ref{['eq:EBH']} for two atoms in an infinite lattice as a function of the nearest-neighbor interaction strength $V$ for (a) $U\gg J$ and (b) $U\ll-J$. The energies correspond either to the continuum spectrum of the scattering states (the shaded bands) or to self-bound states (solid and dashed lines). There are three relevant regions of the coupling $V$: in (I), the ground state of $H^+$ is a scattering state, in contrast to (II) and (III), where the ground state of $H^+$ is the self-bound state. The difference between (II) and (III) is that in the latter, there exists an excited, self-bound eigenstate of $H^-$ with energy close to the energy of a ground state of $H^+$. The panels in the middle show three pairs of eigenstates for three different values of nonlocal attraction $V$ corresponding to aforementioned regions (marked in the upper panels by $c_I$, $c_{II}$ and $c_{III}$). We show the ground states of the Hamiltonians $H^+$ (blue lines with circles) and the eigenstates of $H^-$ (yellow lines with triangles) with the energy closest to the energy of $H^+$ GS. The bottom panel (d) shows the coefficients $\alpha$ characterizing the two-body self-bound eigenstates. In region II there is no self-bound eigenstate of $H^-$ (solid yellow lines with triangles) with $\alpha$ similar to that of $H^+$.
• Figure 3: Super-Tonks-Girardeau quench diagram for the two-body system. In region I, the ground state of the system is a scattering state (Scat), which is stable in sTG quench. Region II corresponds to self-bound states (Self-b), which expand after the quench to strong attraction. Finally, in region III the bound ground state survives the change of interactions and is stable after the quench.
• Figure 4: Fidelity $F(\beta)$ between the ground state of $H^+$ and eigenstates of $H^-$ for $N=3$ atoms in lattice with $N_s=31$ sites, with $|U|=40J$. For $V=0$ (scattering state) and $V=-8J$ (deeply self-bound state), there is a highly excited eigenstate, the superpartner, practically equal to $|H_0^+\rangle$. In contrast, the ground state of $H^+$ with an intermediate value of $V=-1.97J$ (weakly self-bound) is a superposition of several states with different energies, which makes it unstable after the quench.
• Figure 5: Density profiles (top panels) and density-density correlations (bottom panels) as a function of time for the quenched system initiated in the ground state of $H^+$. The nearest-neighbor interaction strengths are (a,d) $V=0$, (b,e) $V=-1.97J$, and (c,f) $V=-8J$. It can be seen that for the weak (a, d) and very strong (c, f) attraction, both the density profile and the correlations remain unchanged for a long time. At the same timescale, the weakly bound state corresponding to $V=-1.97J$ fully evaporates (b, e). All figures correspond to the number of atoms $N=3$ and $|U|=40J$.