Fabien Alet

Quantum critical scaling of fidelity susceptibility

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite size analysis applied to the so obtained numerical results confirm the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy’s second derivative, that can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.

Cluster Monte Carlo algorithm for the quantum rotor model.

We propose a highly efficient worm-like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the algorithm even in the presence of disorder. For the pure quantum rotor model with mu=0, the algorithm yields high- precision estimates for the critical point K(c)=0.333 05(5) and the correlation length exponent nu=0.670(3). For the disordered case, mu=1 / 2+/-1 / 2, we find nu=1.15(10).

Valence bond entanglement entropy.

We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.

SU(N) Heisenberg model on the square lattice: A continuous-N quantum Monte Carlo study

A quantum phase transition is typically induced by tuning an external parameter that appears as a coupling constant in the Hamiltonian. Another route is to vary the global symmetry of the system, generalizing, e.g., SU(2) to SU(N). In that case, however, the discrete nature of the control parameter prevents one from identifying and characterizing the transition. We show how this limitation can be overcome for the SU(N) Heisenberg model with the help of a singlet projector algorithm that can treat N continuously. On the square lattice, we find a direct, continuous phase transition between Neel-ordered and crystalline bond-ordered phases at Nc=4.57(5) with critical exponents z=1 and beta/nu=0.81(3).

Hindered magnetic order from mixed dimensionalities in CuP2O6

We present a combined experimental and theoretical study of the spin-1/2 compound CuP

Impurity spin texture at a deconfined quantum critical point

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Gauge theory picture of an ordering transition in a dimer model.

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Many-body localization: An introduction and selected topics

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Phase diagram of an extended classical dimer model

that features a network of two-dimensional (2D) antiferromagnetic (AFM) square planes, interconnected via one-dimensional (1D) AFM spin chains. Magnetic susceptibility, high-field magnetization, and electron spin resonance (ESR) data, as well as microscopic density-functional band-structure calculations and subsequent quantum Monte-Carlo simulations, show that the coupling

Doping quantum dimer models on the square lattice

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