Solving conformal defects in 3D conformal field theory using fuzzy sphere regularization.

Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study, especially in dimensions higher than two. Here, we demonstrate that the recently-developed theoretical scheme, fuzzy (non-commutative) sphere regularization, provides a powerful lens through which one can dissect the defect of 3D CFTs in a transparent way. As a notable example, we study the magnetic line defect of 3D Ising CFT and clearly demonstrate that it flows to a conformal defect fixed point. We have identified 6 low-lying defect primary operators, including the displacement operator, and accurately extract their scaling dimensions through the state-operator correspondence. Moreover, we also compute one-point bulk correlators and two-point bulk-defect correlators, which show great agreement with predictions of defect conformal symmetry, and from which we extract various bulk-defect operator product expansion coefficients. Our work demonstrates that the fuzzy sphere offers a powerful tool for exploring the rich physics in 3D defect CFTs.

Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Spheres.

Conformal field theory (CFT) plays a crucial role in the study of various critical phenomena. While much attention has been paid to the critical exponents of different universalities, which correspond to the conformal dimensions of CFT primary fields, other important and intricate data such as operator product expansion (OPE) coefficients governing the fusion of two primary fields, have remained largely unexplored, especially in dimensions higher than 2D (or equivalently, 1+1D). Motivated by the recently proposed fuzzy sphere regularization, we investigate the operator content of 3D Ising criticality from a microscopic perspective. We first outline the procedure for extracting OPE coefficients on the fuzzy sphere and then compute 13 OPE coefficients of low-lying CFT primary fields. Our results are highly accurate and in agreement with the numerical conformal bootstrap data of 3D Ising CFT. Moreover, we were able to obtain 4 OPE coefficients, including f_{T_{µν}T_{ρη}ε}, which were previously unknown, thus demonstrating the superior capabilities of our scheme. Expanding the horizon of the fuzzy sphere regularization from the state perspective to the operator perspective opens up new avenues for exploring a wealth of new physics.

Entanglement Hamiltonian of Many-Body Dynamics in Strongly Correlated Systems.

A powerful perspective in understanding nonequilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, much less is known about the refined characteristics of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagating out of equilibrium, from the view of the entanglement Hamiltonian. We investigate quantum quench dynamics of prototypical Bose-Hubbard model using state-of-the-art numerical technique combined with conformal field theory. Before reaching equilibrium, it is found that a current operator emerges in the entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit the subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, the entanglement temperature in steady state is spatially independent, which provides an intuitive trait of equilibrium. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from the perspective of the entanglement Hamiltonian.

Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet.

We study the spin liquid candidate of the spin-1/2 J_{1}-J_{2} Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless U(1) Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion.

Unifying description of competing orders in two-dimensional quantum magnets.

Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. We explore a promising framework in two dimensions, the Dirac spin liquid (DSL) - quantum electrodynamics (QED3) with 4 Dirac fermions coupled to photons. Importantly, its excitations include magnetic monopoles that drive confinement. We address previously open key questions - the symmetry actions on monopoles on square, honeycomb, triangular and kagome lattices. The stability of the DSL is enhanced on triangular and kagome lattices compared to bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on triangular and kagome lattices, including those of monopole excitations, as a guide to numerics and experiments on existing materials. Even when unstable, the DSL helps unify and organize the plethora of ordered phases in correlated two-dimensional materials.

Entanglement signatures of emergent Dirac fermions: Kagome spin liquid and quantum criticality.

Quantum spin liquids (QSLs) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its nonlocality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge-ordered phase.

Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice.

We use large scale quantum Monte Carlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum Monte Carlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.

Bosonic integer quantum Hall effect in an interacting lattice model.

We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry-protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with |σ_{xy}|=2, (ii) two counterpropagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases.

Distinct spin liquids and their transitions in spin-1/2 XXZ kagome antiferromagnets.

By using the density matrix renormalization group approach, we study spin-liquid phases of spin-1/2 XXZ kagome antiferromagnets. We find that the emergence of the spin-liquid phase is independent of the anisotropy of the XXZ interaction. In particular, the two extreme limits-the Ising (a strong S^{z} interaction) and the XY (zero S^{z} interaction)-host the same spin-liquid phases as the isotropic Heisenberg model. Both a time-reversal-invariant spin liquid and a chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show that they evolve continuously into each other by tuning the second- and the third-neighbor interactions. And last, we discuss possible implications of our results for the nature of spin liquid in nearest-neighbor XXZ kagome antiferromagnets, including the nearest-neighbor spin-1/2 kagome antiferromagnetic Heisenberg model.

Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase.

While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.

Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model.

Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.