Cooling arbitrary near-critical systems using hyperbolic quenches

TL;DR

This paper introduces a hyperbolic quench protocol that rapidly prepares ground states of 1+1 dimensional conformal field theories from gapped systems, leveraging symmetry and conformal invariance, and verified through exact and numerical methods.

Contribution

The authors propose a novel hyperbolic quench method for efficiently cooling and preparing ground states of arbitrary 1+1D conformal field theories, extending previous techniques.

Findings

The post-quench stress-energy tensor is uniquely constrained by symmetry.

The system approaches vacuum energy density except along singular lines.

The method conserves entropy even when starting from excited states.

Abstract

We describe a quench protocol that allows the rapid preparation of ground states of arbitrary interacting conformal field theories in $1+1$ dimensions. We start from the ground state of a related gapped relativistic quantum field theory and consider sudden quenches along the space-like trajectories $t^2 - x^2 = T^2_0$ (parameterized by $T_0$) to a conformal field theory. Using only arguments of symmetry and conformal invariance, we show that the post-quench stress-energy tensor of the conformal field theory is uniquely constrained up to an overall scaling factor. Crucially, the $\textit{geometry}$ of the quench necessitates that the system approach the vacuum energy density over all space except the singular lines $x = \pm t$. The above arguments are verified using an exact treatment of the quench for the Gaussian scalar field theory (equivalently, the Luttinger liquid), and numerically for the quantum $O(N)$ model in the large-$N$ limit. Additionally, for the Gaussian theory, we find in fact that even when starting from certain excited states, the quench conserves entropy, and is thus also suitable for rapidly preparing excited states. Our methods serve as a fast, alternative route to reservoir-based cooling to prepare quantum states of interest.