Lukas Weber, Andreas Honecker, Bruce Normand, Philippe Corboz, Frédéric Mila, Stefan Wessel
SciPost Phys. 12, 054 (2022) ·
published 8 February 2022

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The phase diagrams of highly frustrated quantum spin systems can exhibit firstorder quantum phase transitions and thermal critical points even in the absence of any longranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loopupdate scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spintrimer basis are signproblemfree when the intertrimer couplings are fully frustrated. This model features a firstorder quantum phase transition, from which a line of firstorder transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the firstorder line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.
Saeed S. Jahromi, Román Orús, Didier Poilblanc, Frédéric Mila
SciPost Phys. 9, 092 (2020) ·
published 29 December 2020

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We study the zerotemperature phase diagram of the spin$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangledpair state and infinite projected entangledsimplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spinliquid (QSL) groundstate of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical latticenematic phase that breaks rotational symmetry in real space through a firstorder quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.
SciPost Phys. 6, 033 (2019) ·
published 14 March 2019

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Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin1/2 ladders and spin1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum loop model. Building on the constraints imposed on the dimers, we develop a Density Matrix Renormalization Group algorithm that takes full advantage of the relatively small Hilbert space that only grows as Fibonacci number. We further show that both models can be mapped rigorously onto a hardboson model first studied by Fendley, Sengupta and Sachdev [Phys. Rev. B 69, 075106 (2004)], and combining early results with recent results obtained with the present algorithm on this hardboson model, we discuss the full phase diagram of these quantum dimer and quantum loop models, with special emphasis on the phase transitions. In particular, using conformal field theory, we fully characterize the Ising transition and the tricritical Ising end point, with a complete analysis of the boundaryfield correspondence for the tricritical Ising point including partially polarized edges. Finally, we show that the Fibonacci anyon chain is exactly equivalent to special critical points of these models.
SciPost Phys. 5, 030 (2018) ·
published 28 September 2018

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We study the triangularlattice Ising model with dipolar interactions, inspired by its realisation in artificial arrays of nanomagnets. We show that a classical spinliquid forms at intermediate temperatures, and that its behaviour can be tuned by temperature and/or a small lattice distortion between a string Luttinger liquid and a domainwallnetwork state. At low temperature there is a transition into a magnetically ordered phase, which can be firstorder or continous with a crossover in the critical behaviour between PokrovskyTalapov and 2DIsing universality. When the PokrovskyTalapov criticality dominates, the transition is essentially of the Kasteleyn type.
Stefan Wessel, B. Normand, Frédéric Mila, Andreas Honecker
SciPost Phys. 3, 005 (2017) ·
published 18 July 2017

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Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact that the sign problem is basisdependent. Recent studies have shown that passing to a dimer (twosite) basis eliminates the sign problem completely for a fully frustrated spin model on the twoleg ladder. We generalize this result to all partially frustrated twoleg spin1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L=200 rungs (400 spins 1/2) and down to very low temperatures.