Gauge theory and mixed state criticality

Abstract

In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is characterized by the Renyi-2 correlators. In this work, we present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models. In addition to introducing a new type of mixed-state topological phases, we provide models of the criticalities between them, including those with gapless symmetry-protected topological order. We clarify that the ground states of lattice gauge theories are purified states of the corresponding mixed SSB states. Our construction can be applied to any finite gauge theory and offers a framework to study quantum operations between mixed quantum phases.

Figures (1)

• Figure 1: The magnetization squared and entanglement entropy for the mixed state $\varrho$ obtained from the model \ref{['eq:TFI_eff']}, $\varrho= \mathrm{Tr}_{{\cal H}_A}(\rho_0)$. Here, the mixed state $\varrho$ can also be obtained from the ground state $\tilde{\rho}_0$ of \ref{['model 1 unitary gauge']} and applying the decoherence channel, ${\cal E}_{ZZ}$, $\varrho = {\cal E}_{ZZ}(\tilde{\rho}_0)$. The corresponding state $|\varrho\rangle\!\rangle$ in the double state picture can be obtained numerically by the density matrix renormalization group (DMRG) using iTensor library itensoritensor-r0.3. The magnetization squared can be evaluated as $\langle M^2 \rangle\equiv \langle\!\langle \varrho| (\sum_j \sigma^z_{j-1/2})^2 |\varrho\rangle\!\rangle$. The entanglement entropy ($S_A$) is calculated from $|\varrho\rangle\!\rangle$ by tracing out the half of the chain in the double Hilbert space. Both numerical simulations are implemented with open boundary conditions.