Rapidly-converging methods for the location of quantum critical points from finite-size data

Abstract

We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster convergence rate as compared to currently used methods. The approaches are valid in any spatial dimension and for any value of the dynamic exponent. We demonstrate the effectiveness of our methods both analytically on the basis of the one dimensional XY model, and numerically considering c = 1 transitions occurring in non integrable spin models. In particular, we show that these general methods are able to locate precisely the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state properties on relatively small systems.

9 pages, 2 EPS figures, RevTeX style. Updated to published version

References in corpus (8)

• The density-matrix renormalization group
• The Loop Algorithm
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Twist Boundary Conditions of Quantum Spin Chains near the Gaussian Fixed Points
• On $c=1$ critical phases in anisotropic spin-1 chains
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods

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• Scaling of entanglement support for Matrix Product States
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• Detecting Quantum Critical Points using Bipartite Fluctuations
• Finite-size scaling of string order parameters characterizing the Haldane phase
• Parity quantum numbers in the Density Matrix Renormalization Group
• Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
• Resonant two-site tunnelling dynamics of bosons in a tilted optical superlattice
• Quantum phase transition without gap opening
• Finding critical points using improved scaling Ansaetze
• Optimal quasi-free approximation:reconstructing the spectrum from ground state energies