Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories

Abstract

Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest both from a fundamental and technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models -- the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin-$S$ $\mathrm{U}(1)$ quantum link model. By tuning a confining parameter in these models, it is found that \textit{branch} (\textit{manifold}) DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.

Figures (3)

• Figure 1: The return rates and order parameter of the quench of the inverse-square long-range LR-TFIC \ref{['eq:tfim']} from $h_\text{i} = 0$ to (a) $h_\text{f} = 1.25J < h_\text{c}^\text{d}$ and (b) $h_\text{f} = 2.5J > h_\text{c}^\text{d}$. Note that the values of the return rate go to twice the time as those of the order parameter: this is since we can calculate the return rate at time $2t$ using the wave function at time $t$ using the doubling trick (see text).
• Figure 2: The return rates and order parameter of the quench of the transverse field in the two-dimensional square-lattice transverse-field Ising model \ref{['eq:2d-ising']} on a cylindrical geometry with circumference $L_y = 6$, from $h_\text{i} = 0$ to (a) $h_\text{f} = 1.3J < h_\text{c}^\text{d}$ and (b) $h_\text{f} = 4J > h_\text{c}^\text{d}$.
• Figure 3: The return rates and order parameter of the quench of the spin-$1$$\mathrm{U}(1)$ QLM \ref{['eq:qlm']}, $\mu = 0.1\kappa$, from the positive extreme vacuum $\ket{\psi^+}$ to (a) $g_\text{f} = 0$, (b) $g_\text{f} = 0.6\kappa$ and (c) $g_\text{f} = 1.4\kappa$.