Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols

TL;DR

This paper develops a formalism to analyze finite-temperature topological phase transitions in spin-$j$ systems using the Uhlmann process, revealing temperature-dependent topological regimes and proposing experimental protocols.

Contribution

It derives general formulas for the Uhlmann phase and Loschmidt amplitude for arbitrary spin-$j$ systems and links topological phase transitions to quantized jumps and zeros in these quantities.

Findings

Topological regimes exist only at finite temperatures for certain spins.

The number of TQPTs correlates with the winding number in parameter space.

Experimental protocols for observing these effects are proposed.

Abstract

The Uhlmann process is built on the density matrix of a mixed quantum state and offers a way to characterize topological properties at finite temperatures. We analyze an ideal spin-j quantum paramagnet in a magnetic field undergoing an Uhlmann process and derive general formulae of the Uhlmann phase and Loschmidt amplitude for arbitrary j as the system traverses a great circle in the parameter space. A quantized jump of the Uhlmann phase signifies a topological quantum phase transition (TQPT) of the underlying process, which is accompanied by a zero of the Loschmidt amplitude. The exact results of j=1/2 and j=1 systems show topological regimes that only survive at finite temperatures but not at zero temperature, and the number of TQPTs is associated with the winding number in the parameter space. Our results pave the way for future studies on finite-temperature topological properties, and possible experimental protocols and implications for atomic simulators and digital simulations are discussed.