Quantum spin liquid in a spin-12XYmodel with four-site exchange on the kagome lattice

Abstract

We study the ground state phase diagram of a two-dimensional kagome lattice spin-1/2 XY model (J) with a four-site ring exchange interaction (K) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ring exchange, undergoes a direct transition to a Z2 quantum spin liquid phase at (K/J)c ≈ 22, which is related to the phase proposed by Balents, Girvin and Fisher [Phys. Rev. B, 65 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents z and ν falling in the 3D XY universality class, making it a candidate for an exotic XY* quantum critical point, mediated by the condensation of bosonic spinons.The coveted quantum spin liquid state, proposed more than three decades ago by Fazekas and Anderson [1], remains surprisingly elusive. Although recent experiments [2-4] provide tantalizing evidence of their existence, the scarcity of spin liquid states in microscopic models belies their resistance to theoretical characterization. Even a basic unifying notion for which microscopic ingredients are required to promote spin liquid states in models is muddied. Geometric frustration is the main suspect; recent Density-Matrix Renormalization Group measurements have championed the case for a spin liquid as the long-debated groundstate of the kagome lattice Heisenberg antiferromagnet [5]. However, the apparent discovery of a gapped spin liquid state in quantum Monte Carlo (QMC) simulations of the honeycomb lattice Hubbard model at half filling seems to contradict some longheld notions for where spin liquids might lie [6]. The extensive theoretical framework [7][8][9][10], developed over decades, continues to undergo refinement [11][12][13] motivated by these and other discoveries from large-scale computer simulations of a relatively small number of models.Part of the difficulty in finding models that harbor spin liquids in two-dimensions (2D) and higher is the fact the important ingredient of frustration typically leads to the infamous sign problem and preclusion of the model from being studied by scalable QMC techniques. A significant development in this front came in 2002, when Balents et. al.[14] proposed a sign-problem free Hamiltonian of spins on the kagome lattice which gives rise to a Z 2 spin liquid phase. Away from their exactly soluble point, the spin liquid appears to be robust, as several models containing XY terms and constrained potentials have now shown evidence of this spin liquid ground state [15][16][17]. In this paper, we demonstrate that a Z 2 spin liquid phase can also be stabilized in a model with competition between purely kinetic terms, namely two-site XY and four-site "ring" exchange interactions. This Hamiltonian is amenable to large-scale quantum Monte Carlo (QMC) studies, which allows us to characterize the spin liquid state -and the quantum phase transition into this state -in great detail. We find that there exists a single di- rect quantum phase transition into the spin liquid from the superfluid phas...

Gapless spin-liquid phase in the kagome spin-12Heisenberg antiferromagnet

“…Introduction. The spin-1/2 quantum Heisenberg antiferromagnet (QHAF) on the kagome lattice provides a conducive environment to stabilize a quantum paramagnetic phase of matter down to zero temperature, [1][2][3] a fact that has been convincingly established theoretically from several studies, including exact diagonalization, 4-8 series expansion, 9,10 quantum Monte Carlo, 11 and analytical techniques. 12 The question of the precise nature of the spin-liquid state of the kagome spin-1/2 QHAF has been intensely debated on the theoretical front, albeit without any definitive conclusions.…”

Nature of the phases in the frustratedXYmodel on the honeycomb lattice

“…There, evidence was found supporting the existence of a spin liquid surrounded by two magnetically ordered states, namely, an antiferromagnetic (collinear) state at lower (higher) J 2 /J 1 . The spin-liquid phase was suggested to be gapless and characterized by a distinctive parameter dependent feature in the momentum distribution n(k), similar to a Bose surface, thus suggesting the presence of an exotic Bose metal [20,24,[26][27][28][29][30][31].…”

Quantum spin superfluid from Bose-Einstein condensation of spinons in pyrochlore spin ice

“…Note added: While we were finishing this manuscript, we became aware of a recent work based on quantum Monte-Carlo numerical simulation of pyrochlore spin ice at finite temperature and magnetic field along [111] direction at J ±± = J z± = 0 [32].In their case, they found a 'monopole superfluid' state, but which manifests a confined Higgs condensed state of spinons, corresponding to an XY ferromagnet order.Interestingly though, their monopole superfluid state in the zero field limit occurs on the same part of J ± axis as ours and they also obtain a superfluid density proportional to |J ⊥ | ≡ |J ± |.Our work investigates analytically the case at finite J ±± , J z± at zero field and finds a truly 'fluidic' spin superfluid state with no magnetic order, manifesting a deconfined state of Higgs condensed spinons.The singularity in |Ψ| 2 at J ±± = 0 noted in [21] along the |J c ± | < |J ± | < |J crit ± | segment in Fig.2 marks a deconfinement-confinement transition of the spinons from our QSSF state to the XY ferromagnet of [32].Our work is thus distinct but complements that of [32].We also just learned that a quantum spin superfluid state from condensation of hard-core bosons rather than spinons was found in pyrochlore using quantum Monte-Carlo simulation a while ago [33] which also indicates a first order superfluid transition.These works estimate that |J c ± | 0.104J zz .A spin superfluid state in 2d spin system (kagomé spin 1/2 XY model) was also deduced from quantum Monte-Carlo simulation, but requires ring-exchange interaction and has a second-order superfluid phase transition within XY universality class [34].…”