https://indico.imsc.res.in/event/11

Mpemba effect occurs when a system, residing far away from the steady state, relaxes faster than a relatively nearer state. We first discuss how such an effect works for the quantum state in an open system. We then address the question of detecting such an effect through relevant observables. We further look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a non-trace preserving map, trace distance measure can not serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a dressed distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. We further show how to observe genuine Mpemba effect for operators. References: 1. Detection of Mpemba effect through good observables in open quantum systems Pitambar Bagui, Arijit Chatterjee, and Bijay Kumar Agarwalla [arXiv] (Accepted in Phys. Rev. B) 2. Accelerated relaxation and Mpemba-like effect for operators in open quantum systems, Pitambar Bagui, Arijit Chatterjee, and Bijay Kumar Agarwalla [arXiv] (Accepted in Phys. Rev. A Letter) 3. Quantum Mpemba effect for operators in open systems Pitambar Bagui and Bijay Kumar Agarwalla [arXiv]

We construct a ℤ2×ℤ2 gauge theory coupled to matter on a one-dimensional chain, aiming to study the ground-state physics in the Gauss law subspace. We show that the theory in the Gauss law subspace has a U(1) symmetry whose generator commutes with lattice translations, but anticommutes with the lattice reflection operator. This leads to a Lieb-Schultz-Mattis (LSM) theorem that always rules out a trivial gapped ground state in the Gauss law subspace, if the hamiltonian is invariant under translations and reflection. Any point in the parameter space must realize either a spontaneously symmetry broken (SSB) ground state, or a gapless ground state. Imposing the Gauss law is pivotal for the existence of the U(1) symmetry, and hence of the LSM theorem. We thus demonstrate a novel mechanism to obtain an LSM-type theorem, wherein the symmetry responsible for the theorem originates from the kinematic constraints of a gauge theory. We identify a point in the parameter space at which the system is gapless. At the gapless point, the excitations admit a description in terms of free Dirac fermions with a constraint on the total fermion number. The asymptotic behavior of the two-point correlation function of the simplest local gauge-invariant quantity at the gapless point is found to be ∝cos(πr)r−2/9, where r is the lattice separation between the two points. This model is also a natural platform to study phase diagram topological defects residing in families of SSB phases.

https://indico.imsc.res.in/event/11

Continuous measurement of quantum systems provides a standard route to quantum trajectories through the successive acquisition of information which further results in measurement back-action. In this work, we harness this back-action as a resource for global U(1) symmetry restoration where continuous measurement is combined with a U(1)-preserving unitary evolution. Starting from a U(1) symmetry-broken initial state, we simulate quantum trajectories generated by continuous measurements of both global and local observables. We show that under global monitoring, states containing superpositions of distant charge sectors restore symmetry faster than those involving nearby sectors. We establish the universality of this behavior across different measurement protocols. Finally, we demonstrate that local monitoring can further accelerate symmetry restoration for certain states that relax slowly under global monitoring. Reference: Measurement induced faster symmetry restoration in quantum trajectories, Katha Ganguly, Bijay Kumar Agarwalla [arXiv]