Extracting quantum-critical properties from directly evaluated enhanced perturbative continuous unitary transformations

Abstract

Directly evaluated enhanced perturbative continuous unitary transformations (deepCUTs) are used to calculate non-perturbatively extrapolated numerical data for the ground-state energy and the energy gap. The data coincides with the perturbative series up to the order with respect to which the deepCUT is truncated. We develop a general scheme to extract quantum-critical properties from the deepCUT data based on critical scaling and a strict correspondence between the truncation used for deepCUT and the length scale of correlations at the critical point. We apply our approach to transverse-field Ising models (TFIMs) as paradigmatic systems for quantum phase transitions of various universality classes depending on the lattice geometry and the choice of antiferromagnetic or ferromagnetic coupling. In particular, we focus on the quantum phase diagram of the bilayer antiferromagnetic TFIM on the triangular lattice with an Ising-type interlayer coupling. Without a field, the model is known to host a classically disordered ground state, and in the limit of decoupled layers it exhibits the 3d-XY 'order by disorder' transition of the corresponding single-layer model. Our starting point for the unknown parts of the phase diagram is a high-order perturbative calculation about the limit of isolated dimers where the model is in a gapped phase.

31 pages

References in corpus (13)

• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Effective models for gapped phases of strongly correlated quantum lattice models
• Dispersive Excitations in the One-Dimensional Ionic Hubbard Model
• A generalized perspective on non-perturbative linked cluster expansions
• Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model
• Singlet exciton condensation and bond-order-wave phase in the extended Hubbard model
• Truncation errors in self-similar continuous unitary transformations
• Projective cluster-additive transformation for quantum lattice models
• Series expansions in closed and open quantum many-body systems with multiple quasiparticle types