Topological and Geometric Universal Thermodynamics in Conformal Field Theory
| Autor: | Hai Lin, Hao-Xin Wang, Wei Li, Lei Chen |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Strongly Correlated Electrons (cond-mat.str-el) Statistical Mechanics (cond-mat.stat-mech) Conformal field theory Physical constant Boundary (topology) Thermodynamics FOS: Physical sciences Mathematical Physics (math-ph) Topology 01 natural sciences Mathematics::Geometric Topology 010305 fluids & plasmas Condensed Matter - Strongly Correlated Electrons Singularity Real projective plane 0103 physical sciences Connection (algebraic framework) 010306 general physics Central charge Topological conjugacy Condensed Matter - Statistical Mechanics Mathematical Physics |
| DOI: | 10.48550/arxiv.1801.07635 |
| Popis: | Universal thermal data in conformal field theory (CFT) offer a valuable means for characterizing and classifying criticality. With improved tensor network techniques, we investigate the universal thermodynamics on a nonorientable minimal surface, the crosscapped disk (or real projective plane, $\mathbb{RP}^2$). Through a cut-and-sew process, $\mathbb{RP}^2$ is topologically equivalent to a cylinder with rainbow and crosscap boundaries. We uncover that the crosscap contributes a fractional topological term $\frac{1}{2} \ln{k}$ related to nonorientable genus, with $k$ a universal constant in two-dimensional CFT, while the rainbow boundary gives rise to a geometric term $\frac{c}{4} \ln{\beta}$, with $\beta$ the manifold size and $c$ the central charge. We have also obtained analytically the logarithmic rainbow term by CFT calculations, and discuss its connection to the renowned Cardy-Peschel conical singularity. Comment: 4 pages + references, 7 figures, 2 tables, supplementary material; published version |
| Databáze: | OpenAIRE |
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