Scaling at quantum phase transitions above the upper critical dimension

Abstract

The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension following the recently introduced Q-FSS formalism for thermal phase transitions. Contrary to long-standing belief, the correlation sector is affected by dangerous irrelevant variables. The presented formalism recovers a generalized hyperscaling relation and FSS form. Using this new FSS formalism, we determine the full set of critical exponents for the long-range transverse-field Ising chain in all criticality regimes ranging from the nearest-neighbor to the long-range mean field regime. For the same model, we also explicitly confirm the effect of dangerous irrelevant variables on the characteristic length scale.

arXiv comment28 pages, 5 figures. This version fixes some typos, specifically in Eq. 5 and regarding some of the short-range exponents in Tab. 3 and the captions of Fig. 1 and Fig. 2. We thank M. Henkel for pointing out the typos in the short-range exponents

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• Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Finite-Size Scaling of the majority-voter model above the upper critical dimension
• On a previously unpublished work with Ralph Kenna