Fractionalized conductivity and emergent self-duality near topological phase transitions
TL;DR: The study of a strongly correlated quantum phase transition between a topological state shows that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition, indicating the presence of the elusive vison particles.
Abstract: The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $\mathbb{Z}_2$ quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.
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TL;DR: In this paper, the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems is discussed.
Abstract: We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.
1,347 citations
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TL;DR: In the past few years, increasing evidence has accumulated for a number of materials suggesting that they have characteristics strongly reminiscent of those expected for a quantum spin liquid as mentioned in this paper, although there is not yet entirely convincing experimental evidence that any particular material has a spin liquid ground state.
Abstract: Spin liquids are quantum phases of matter that exhibit a variety of novel features associated with their topological character. These include various forms of fractionalization - elementary excitations that behave as fractions of an electron. While there is not yet entirely convincing experimental evidence that any particular material has a spin liquid ground state, in the past few years, increasing evidence has accumulated for a number of materials suggesting that they have characteristics strongly reminiscent of those expected for a quantum spin liquid.
229 citations
Journal Article•
TL;DR: These results, together with the equivalence between hard-core bosons and S=1/2 spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-1/ 2 model with no special conservation laws.
Abstract: We study a model of hard-core bosons with short-range repulsive interactions at half filling on the kagome lattice. Using quantum Monte Carlo numerics, we find that this model shows a continuous superfluid-insulator quantum phase transition, with exponents $z=1$ and $\ensuremath{
u}\ensuremath{\approx}0.67(5)$. The insulator, ${\mathcal{I}}^{*}$, exhibits short-ranged density and bond correlations, topological order, and exponentially decaying spatial vison correlations, all of which point to a ${Z}_{2}$ fractionalized phase. We estimate the vison gap in ${\mathcal{I}}^{*}$ from the temperature dependence of the energy. Our results, together with the equivalence between hard-core bosons and $S=1/2$ spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-$1/2$ model with no special conservation laws.
34 citations
TL;DR: In this paper , the authors present large-scale quantum Monte Carlo simulation results on an extension of the triangular lattice quantum dimer model with terms in the Hamiltonian annihilating and creating single dimers.
Abstract: Quantum dimer models are known to host topological quantum spin liquid phases, and it has recently become possible to simulate such models with Rydberg atoms trapped in arrays of optical tweezers. Here, we present large-scale quantum Monte Carlo simulation results on an extension of the triangular lattice quantum dimer model with terms in the Hamiltonian annihilating and creating single dimers. We find distinct odd and even [Formula: see text] spin liquids, along with several phases with no topological order: a staggered crystal, a nematic phase, and a trivial symmetric phase with no obvious broken symmetry. We also present dynamic spectra of the phases, and note implications for experiments on Rydberg atoms.
25 citations
Journal Article•
TL;DR: In this paper, the authors study the extended $XXZ$ model on the kagome lattice and show that a spin liquid phase with effective Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid, and ferromagnet.
Abstract: Employing large-scale quantum Monte Carlo simulations, we study the extended $XXZ$ model on the kagome lattice. A ${\mathbb{Z}}_{2}$ quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid, and ferromagnet. This ${\mathbb{Z}}_{2}$ spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the transition between the stripe solid and ferromagnet. However, the transition between a spin liquid and ferromagnet is found to be continuous and belongs to the 3D $X{Y}^{*}$ universality class associated with the condensation of spinons. The transition between a spin liquid and stripe solid appears to be continuous and associated with the condensation of visons.
12 citations
References
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TL;DR: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Unitary transformation can be done by joining excitations in pairs and observing the result of fusion.
4,920 citations
TL;DR: This work observes a quantum phase transition in a Bose–Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential, and can induce reversible changes between the two ground states of the system.
Abstract: For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system.
4,467 citations
TL;DR: In this article, the authors presented variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.
Abstract: This Letter presents variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.
3,734 citations
TL;DR: The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation for the formation of the Hall plateau in magnetotransport of high-mobility, two-dimensional electrons as mentioned in this paper.
Abstract: A quantized Hall plateau of ${\ensuremath{\rho}}_{\mathrm{xy}}=\frac{3h}{{e}^{2}}$, accompanied by a minimum in ${\ensuremath{\rho}}_{\mathrm{xx}}$, was observed at $Tl5$ K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is $\frac{1}{3}$ filled. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation.
3,528 citations
Book•
02 Jan 1992
TL;DR: In this paper, the authors presented variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.
Abstract: This Letter presents variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.
3,047 citations