Abstract
We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of Z_3Z3 parafermion or u(1)_6u(1)6 conformal field theories (CFTs). These correspond either to non-trivial permutation invariants or block diagonal invariants, that one can understand in terms of anyon condensation. In terms of lattice parafermion operators, the constructed models correspond to parafermion chains with many-body terms. Our construction is based on how the partition function of a CFT depends on symmetry sectors and boundary conditions. This enables to write the partition function corresponding to one modular invariant as a linear combination of another over different sectors and boundary conditions, which translates to a general recipe how to write down a microscopic model, tuned to criticality. We show that the scheme can also be extended to construct critical generalizations of kk-state clock type models.
Highlights
We find that when many-body terms are comparable to local chemical potential-like terms, the chains are critical and described by the non-diagonal modular invariant partition functions of a conformal field theories (CFTs) that is product of some number of Z3 parafermion or u(1)6 CFTs
Before applying this strategy to construct microscopic models for criticality in Potts-type models, we review briefly the connection to anyon condensation that provides an easy way to predict when such constructions might be possible without knowing all the modular invariant partition functions
We have constructed several new microscopic clock-type models that by construction exhibit exotic critical points described by CFTs not considered previously in the literature
Summary
At a quantum critical point two distinct phases of matter coexist. A remarkable feature of 1D systems is that such special points in the phase diagram are in general described by a field theory with conformal symmetry – a conformal field theory (CFT) [1, 2]. The system exhibits a universal behavior regardless of the underlying microscopic model, i.e. what are the local degrees of freedom and how they interact This universal description at the critical point enables to determine what phases of matter appear in the vicinity of the critical point when the system is perturbed away from it. We focus here on 3-state Potts models, where the local degrees of freedom are not spins, but clock variables, and construct generalizations that exhibit critical points whose critical behavior has not been previously discussed in the literature. The recent focus on parafermions arises not from themselves though, but from their collective behavior Were they to hybridize in a 2D array, they could realize a state that hosts the coveted Fibonacci anyons that are universal for quantum computation [14]. Before proceeding to the actual constructions and the physics underlying them, we summarize our main results – the microscopic generalizations of the 3-state Potts models and the exotic critical points they exhibit
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
