Finite-Size Scaling Theory at a Self-Dual Quantum Critical Point

Abstract

The nondivergence of the generalized Grüneisen ratio (GR) at a quantum critical point (QCP) has been proposed to be a universal thermodynamic signature of self-duality. In this work, we study how the Kramers-Wannier-type self-duality manifests itself in the finite-size scaling behavior of thermodynamic quantities in the quantum critical regime. While the self-duality cannot be realized as a unitary transformation in the total Hilbert space for the Hamiltonian with the periodic boundary condition, it can be implemented in certain symmetry sectors with proper boundary conditions. Therefore, the GR and the transverse magnetization of the one-dimensional transverse-field Ising model exhibit different finite-size scaling behaviors in different sectors. This implies that the numerical diagnosis of self-dual QCP requires identifying the proper symmetry sectors.

arXiv comment5 pages, 3 figures; v2: slightly revised, accepted version

References in corpus (6)

• Is the Composite Fermion a Dirac Particle?
• Universally diverging Grueneisen parameter and the magnetocaloric effect close to quantum critical points
• Topological Characterization of Extended Quantum Ising Models
• Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in Transverse Magnetic Field
• Crossovers and critical scaling in the one-dimensional transverse-field Ising model
• Universal Thermodynamic Signature of Self-dual Quantum Critical Points

Cited by in corpus (4)

• Universal Thermodynamic Signature of Self-dual Quantum Critical Points
• Analytical results for the unusual Grüneisen ratio in the quantum Ising model with Dzyaloshinskii-Moriya interaction
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality