# The Adiabatically Deformed Ensemble: Engineering Non-Thermal States of Matter

## TL;DR

This paper introduces a method to create non-thermal states of matter through adiabatic evolution of thermal ensembles, revealing new physics and potential control over phase transitions in various quantum systems.

## Contribution

It demonstrates a novel approach to engineer non-thermal states via adiabatic passage, with detailed analysis of multiple quantum models using exact, numerical, and approximate methods.

## Key findings

- Non-thermal power-law correlations in spinless fermion chains
- Alteration of topological phase transition temperatures in Kitaev chains
- Stable non-thermal states with unique properties in different models

## Abstract

We propose a route towards engineering non-thermal states of matter, which show largely unexplored physics. The main idea relies on the adiabatic passage of a thermal ensemble under slow variations of the system Hamiltonian. If the temperature of the initial thermal ensemble is either zero or infinite the ensemble after the passage is a simple thermal one with the same vanishing or infinite temperature. However, for any finite non-zero temperature intriguing non-thermal ensembles can be achieved. We exemplify this in: (a) a single oscillator (b) a dimerized interacting one dimensional chain of spinless fermions, (c) a BCS-type superconductor and (d) the topological Kitaev chain. We solve these models with a combination of methods; either exactly, numerically using the density matrix renormalization group (DMRG) or within an approximate functional renormalization group (FRG) scheme. The designed states show strongly non-thermal behavior in each of the considered models. For example, for the chain of spinless fermions we exemplify how long ranged non-thermal power-law correlations can be stabilized and for the Kitaev chain we elucidate how the non-thermal ensemble can largely alter the transition temperature separating topological and trivial phases.