Universal Topological Power Transfer with Arbitrarily Large Chern Number in Driven Quantum Spin Chains

TL;DR

This paper demonstrates a universal topological power transfer mechanism in driven quantum spin chains, enabling arbitrarily large, quantized frequency conversion ratios controlled by system parameters.

Contribution

It introduces a method to achieve large Chern numbers and tunable topological frequency conversion in interacting quantum spin chains with variable chain length and anisotropy.

Findings

Chern number increases with chain length and anisotropy.

Universal dependency of critical points on chain length parity.

Mechanism for arbitrarily large, quantized power transfer in quantum spin chains.

Abstract

Topological frequency converters exploit a quantized transfer of power between two driving fields in a quantum system, a phenomenon topologically protected by the Chern number of the associated fiber bundle. While realizations with few-spin systems have theoretically demonstrated this effect, the conversion factors have typically been restricted to small integer values. Here, we investigate an interacting $XXZ$ Heisenberg spin-$1/2$ chain driven adiabatically by two magnetic drives with incommensurate frequencies. The Chern number, determined by the degeneracy points enclosed by the adiabatic trajectory, increases systematically with the chain length and can be tuned through the exchange anisotropy, providing direct control of the topological pumping strength. We reveal a universal dependency of the anisotropy and magnetic field strength for odd and even chain lengths of the quantum critical points. This provides a mechanism for a topological frequency converter with an arbitrarily large, quantized conversion ratio in interacting quantum spin chains. The mechanism remains the same for arbitrary coupling regions of the drives.