arXiv subjects

Yan-Cheng Wang

Publications and source records attributed to Yan-Cheng Wang.

35 records · Page 2Linked to original sources

arXiv2022

Triangular lattice quantum dimer model with variable dimer density

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 $\mathbb{Z}_2$ 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.

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arXiv2022

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

We develop a nonequilibrium increment method in quantum Monte Carlo simulations to obtain the Rényi entanglement entropy of various quantum many-body systems with high efficiency and precision. To demonstrate its power, we show the results on a few important yet difficult $(2+1)d$ quantum lattice models, ranging from the Heisenberg quantum antiferromagnet with spontaneous symmetry breaking, the quantum critical point with O(3) conformal field theory (CFT) to the toric code $\Z_2$ topological ordered state and the Kagome $\Z_2$ quantum spin liquid model with frustration and multi-spin interactions. In all these cases, our method either reveals the precise CFT data from the logarithmic correction or extracts the quantum dimension in topological order, from the dominant area law in finite-size scaling, with very large system sizes, controlled errorbars and minimal computational costs. Our method therefore establishes a controlled and practical computation paradigm to obtain the difficult yet important universal properties in highly entangled quantum matter.

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arXiv2022

Scaling of disorder operator at deconfined quantum criticality

We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.

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arXiv2022

Scaling of entanglement entropy at deconfined quantum criticality

We develop a nonequilibrium increment method to compute the Rényi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that at an conformally-invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where although we still observe similar scaling behavior but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with positivity condition of the Rényi entanglement entropy, which holds for unitary conformal field theories(CFT). Our results unambiguously reveal fundamental differences between DQC and quantum critical points(QCPs) described by unitary CFTs.

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arXiv2021

Fractionalized conductivity and emergent self-duality near topological phase transitions

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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arXiv2021

Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality

We study disorder operator, defined as a symmetry transformation applied to a finite region, across a continuous quantum phase transition in $(2+1)d$. We show analytically that at a conformally-invariant critical point with U(1) symmetry, the disorder operator with a small U(1) rotation angle defined on a rectangle region exhibits power-law scaling with the perimeter of the rectangle. The exponent is proportional to the current central charge of the critical theory. Such a universal scaling behavior is due to the sharp corners of the region and we further obtain a general formula for the exponent when the corner is nearly smooth. To probe the full parameter regime, we carry out systematic computation of the U(1) disorder parameter in the square lattice Bose-Hubbard model across the superfluid-insulator transition with large-scale quantum Monte Carlo simulations, and confirm the presence of the universal corner correction. The exponent of the corner term determined from numerical simulations agrees well with the analytical predictions.

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arXiv2021

Nonlocal effects of low-energy excitations in quantum-spin-liquid candidate Cu$_3$Zn(OH)$_6$FBr

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.

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arXiv2021

Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid

Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a unique playground for studying the relation between single-anyon and multi-anyon continuum spectra. However, as the prototypical correlated system with local constraints, the generic solution of QDM at different lattice geometry and parameter regimes is still missing due to the lack of controlled methodologies. Here we obtain, via the newly developed sweeping cluster quantum Monte Carlo algorithm, the excitation spectra in different phases of the triangular lattice QDM. Our results reveal the single vison excitations inside the $Z_2$ quantum spin liquid (QSL) and its condensation towards the $\sqrt{12}\times\sqrt{12}$ valence bond solid (VBS), and demonstrate the translational symmetry fractionalization and emergent O(4) symmetry at the QSL-VBS transition. We find the single vison excitations, whose convolution qualitatively reproduces the dimer spectra, are not free but subject to interaction effects throughout the transition. The nature of the VBS with its O(4) order parameters are unearthed in full scope. Our approach opens the avenue for generic solution of the static and dynamic properties of QDMs and has relevance towards the realization and detection of fractional excitations in programmable quantum simulators.

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arXiv2021

Vestigial anyon condensation in kagome quantum spin liquids

We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a $\mathbb Z_2\boxtimes\mathbb Z_2$ topological order to a $\mathbb Z_2$ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.

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arXiv2020

Evidence for the topological order in a kagome antiferromagnet

A Z2 quantum spin liquid hosts one of the simplest topological orders and exhibits many exotic properties due to long-range quantum entanglements. Its elementary excitations are anyons such as spinons carrying fractionalized spin quantum number and visons carrying emergent Z2 gauge flux. However, experimental detection of these anyons remains elusive. The difficulties lie not only in the fact that there exists few candidates for Z2 quantum spin liquids but also in that visons are magnetically inert hence immune to available experimental techniques. Here we have studied the spin excitations and specific heats of kagome-lattice antiferromagnet Cu$_4$(OH)$_6$FBr and Cu$_3$Zn(OH)$_6$FBr, which consists of two-dimensional Cu$^{2+}$ kagome layers with either Cu$^{2+}$ or Zn$^{2+}$ ions in between. By combining the first principle calculations and inelastic neutron scattering data in the former, we show that the dominate couplings in Cu$_4$(OH)$_6$FBr are between the nearest neighbor spins within the kagome planes, and the kagome and interlayer spin systems are essentially decoupled above the antiferromagnetic transition temperature. The intrinsic spin excitations and specific heats of the kagome layers for Cu$_3$Zn(OH)$_6$FBr are thus derived by removing the contributions from the residual interlayer Cu$^{2+}$ magnetic impurities. Accordingly, the kagome spin system exhibits spin continuum with momentum-dependent spin gap and a large magnetic entropy at low temperature that is insensitive to magnetic field, which can be understood as the evidences of spinons and visons in this kagome quantum spin liquid candidate. Our results suggest the existence of the Z2 anyons in the material, and therefore provide a comprehensive set of evidences for the Z2 topological order in kagome quantum spin liquid and bring their choreographed entanglement dances to the stage of real materials.

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arXiv2018

Bosonic SET to SPT Transition under Dyonic LSM Theorem

Employing large-scale quantum Monte Carlo simulatoins, we study the phase diagram of a quantum spin model which is subject to the recently developed dyonic Lieb-Shultz-Mattis (LSM) theorem. The theorem predicts there are symmetry enriched/protected topological (SET/SPT) phases in the phase diagram. Our numerical results reveal a first order quantum phase transition between SET and SPT phases, consistent with an anyon condensation mechanism that enforces SPT phase according to the theorem. Also there exists in the phase diagram a symmetry-breaking phase in the form of superfluid (SF). The transition between SET and SF is continuous and that between SPT and SF is first order. Interestingly, the SET, SPT and SF phases meet at a critical endpoint, whose presence can be universally explained via theory contains emergent gauge field coupled to vortex fields, and consequently reveals the exotic feature of our model even beyond the realm of dyonic LSM.

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arXiv2018

Effect of Zn doping on the antiferromagnetism in kagome Cu$_{4-x}$Zn$_x$(OH)$_6$FBr

Barlowite Cu$_4$(OH)$_6$FBr shows three-dimensional (3D) long-range antiferromagnetism, which is fully suppressed in Cu$_3$Zn(OH)$_6$FBr with a kagome quantum spin liquid ground state. Here we report systematic studies on the evolution of magnetism in the Cu$_{4-x}$Zn$_x$(OH)$_{6}$FBr system as a function of $x$ to bridge the two limits of Cu$_4$(OH)$_6$FBr ($x$=0) and Cu$_3$Zn(OH)$_6$FBr ($x$=1). Neutron-diffraction measurements reveal a hexagonal-to-orthorhombic structural change with decreasing temperature in the $x$ = 0 sample. While confirming the 3D antiferromagnetic nature of low-temperature magnetism, the magnetic moments on some Cu$^{2+}$ sites on the kagome planes are found to be vanishingly small, suggesting strong frustration already exists in barlowite. Substitution of interlayer Cu$^{2+}$ with Zn$^{2+}$ with gradually increasing $x$ completely suppresses the bulk magnetic order at around $x$ = 0.4, but leaves a local secondary magnetic order up to $x\sim 0.8$ with a slight decrease in its transition temperature. The high-temperature magnetic susceptibility and specific heat measurements further suggest that the intrinsic magnetic properties of kagome spin liquid planes may already appear from $x>0.3$ samples. Our results reveal that the Cu$_{4-x}$Zn$_x$(OH)$_6$FBr may be the long-thought experimental playground for the systematic investigations of the quantum phase transition from a long-range antiferromagnet to a topologically ordered quantum spin liquid.

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arXiv2018

Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice

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 $XY^*$ 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.

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arXiv2018

Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets

The nontrivialness of quantum spin liquid (QSL) typically manifests in the non-local observables that signifies their existence, however, this fact actually casts shadow on detecting QSL with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating dynamical signature of anyonic excitations and symmetry fractionalization in QSL. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that across the phase transitions from Z2 QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular the translational symmetry fractionalization of the latter, which can be served as the unique dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) X-ray scatterings.

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arXiv2017

Topological Spin Liquid with Symmetry-Protected Edge States

Topological spin liquids are robust quantum states of matter with long-range entanglement and possess many exotic properties such as the fractional statistics of the elementary excitations. Yet these states, short of local parameters like all topological states, are elusive for conventional experimental probes. In this work, we combine theoretical analysis and quantum Monte Carlo numerics on a frustrated spin model which hosts a $\mathbb Z_2$ topological spin liquid ground state, and demonstrate that the presence of symmetry-protected gapless edge modes is a characteristic feature of the state, originating from the nontrivial symmetry fractionalization of the elementary excitations. Experimental observation of these modes on the edge would directly indicate the existence of the topological spin liquids in the bulk, analogous to the fact that the observation of Dirac edge states confirmed the existence of topological insulators.

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arXiv2017

Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices

Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangle and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and does not have an emergent continuous symmetry. Furthermore, our analysis of the order parameter histogram reveals that such different behavior originates from the irrelevance and relevance of anisotropic terms near the QPT in the low-energy effective theory of the two models. The comparison between theoretical analysis and numerical simulation in this work paves the way for scrutinizing investigation of emergent continuous symmetry at classical and quantum phase transitions.

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arXiv2017

Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu$_3$Zn(OH)$_6$FBr

We report a new kagome quantum spin liquid candidate Cu$_3$Zn(OH)$_6$FBr, which does not experience any phase transition down to 50 mK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature ($\sim$ 200 K). A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from $^{19}$F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fractionalization in the fractional quantum Hall state.

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