An exact local mapping from clock-spins to fermions

Abstract

Clock-spin models are attracting great interest, due to both their rich phase diagram and their connection to parafermions. In this context, we derive an exact local mapping from clock-spin to fermionic partition functions. Such mapping, akin to techniques introduced by Fedotov and Popov for spin $\frac{1}{2}$ chains, grants access to well established numerical tools for the perturbative treatment of fermionic systems in the clock-spin framework. Moreover, in one dimension, it allows to use bosonization to access the low energy properties of clock-spin models. Finally, aside from the direct application in clock-spin models, this new mapping enables the conception of interesting fermionic models, based on the clock-spin counterparts.

26 pages, 0 figures, Submission to SciPost

References in corpus (9)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum Quench in the Transverse Field Ising Chain
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Dynamics in the Ising field theory after a quantum quench
• Stability of zero modes in parafermion chains
• Parafermionic conformal field theory on the lattice
• Commensurate and Incommensurate States of Topological Quantum Matter
• Lifshitz point at commensurate melting of 1D Rydberg atoms
• Spontaneous symmetry breaking without ground state degeneracy in generalized $N$-state clock model

Cited by in corpus (2)

• Charging a Dimerized Quantum XY Chain
• Noninteracting tight-binding models for Fock parafermions