The antiferromagnetic spin-1/2 Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large-scale density matrix renormalization group simulations (DMRG) on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum-dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a p-flux free-fermion model [the parton mean-field ansatz of a U(1) Dirac spin liquid]

Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without timereversal symmetry, and it is considered as the parent state of an exotic type of superconductoranyon superconductor. Such exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in 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 (KHM), 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 KHM.PACS numbers: 75.10. Kt ,75.10.Jm, 75.40.Mg, 05.30.Pr Topological order, an exotic state of matter that hosts fractionalized quasiparticles with anyonic braiding statistics, is one of the core topics in modern condensed-matter physics [1]. Quantum spin liquid (QSL) [2] is a prominent example of topological order, which is thought to exist in some frustrated magnets [3]. Among various types of QSL [3][4][5][6][7][8][9][10][11], there is a class of time-reversal symmetry violating QSL called chiral spin liquid (CSL) [12][13][14]. CSL shares some similar properties with fractional quantum Hall effect, however CSL is special for its both possessing topological order and spontaneously time-reversal symmetry breaking.The simplest CSL is the Kalmeyer-Laughlin (KL) CSL (ν = 1/2 Laughlin state) [12], in which spinons obey semionic fractional statistics. It is theoretically shown that if one dopes the KL CSL with holes [15], an exotic type of superconductivity-anyon superconductivity [16]-will emerge. Inspired by the fundamental interest and prospect of finding exotic superconductors, KL CSL has attracted much interest [17][18][19][20][21][22][23][24][25][26][27][28][29]. In past many years, there was no experimental or theoretical evidence supporting the existence of this state until very recently. Several artificial models were found that can host a KL state [26][27][28]. For example, one can directly induce scalar chirality order by a 3-spin parity and time-reversalviolating interaction [28] on a kagome lattice to produce KL state. However, it remains elusive whether the KL state can exist in a system with time-reversal symmetry, which may be more closely related to real materials. It has been suggested that KL state may exist in magnetic frustrated systems through spontaneously breaking time-reversal symmetry [12,17], which are among the most difficult systems for theorists to study exactly.In this Letter, we show that the KL state is the ground state of a frustrated anisotropic kagome Heisenber...

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.

We study the critical properties of the QED3-Gross-Neveu model with 2N flavors of twocomponent Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N = 1, this theory has recently been suggested to be dual to the SU(2) noncompact CP 1 model that describes the deconfined phase transition between the Néel antiferromagnet and the valence bond solid on the square lattice. For N = 2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED3-Gross-Neveu model for all values of N . This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED3 (without scalar-field coupling) unstable at low values of N . The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter = 4 − D. We compute the scalar-field anomalous dimension η φ , the correlation-length exponent ν, as well as the scaling dimension of the flavor-symmetry-breaking bilinearψσ z ψ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

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.

The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL) which can be defined on the honeycomb, square, triangular and kagomé lattices. At low energies, the DSL on all these lattices is described by an emergent Quantum Electrodynamics (QED3) with N f = 4 flavors of Dirac fermions coupled to a U (1) gauge field. However the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom, behave very differently on different lattices. In particular, we show that the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulator. We also show that for DSLs on bipartite lattices, there always exists a monopole that transforms trivially under all microscopic symmetries owing to the existence of a parent SU(2) gauge theory. We connect our results to generalized Lieb-Schultz-Mattis theorems and also derive the timereversal and reflection properties of monopoles. Our results indicate that recent insights into free fermion band topology can also guide the description of strongly correlated quantum matter. CONTENTS

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.

We study the ground states of 2D lattice bosons in an artificial gauge field. Using state of the art DMRG simulations we obtain the zero temperature phase diagram for hardcore bosons at densities n b with flux n φ per unit cell, which determines a filling ν = n b /n φ . We find several robust quantum Hall phases, including (i) a bosonic integer quantum Hall phase (BIQH) at ν = 2, that realizes an interacting symmetry protected topological phase in 2D (ii) bosonic fractional quantum Hall phases including robust states at ν = 2/3 and a Laughlin state at ν = 1/2. The observed states correspond to the bosonic Jain sequence (ν = p/(p + 1)) pointing towards an underlying composite fermion picture. In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation beginning from independent chains, and ramping up interchain couplings. Using time dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Besides the wave-function overlap, we utilize a simple physical signature of these phases, the non-monotonic behavior of a two-point correlation, a direct consequence of edge states in a finite system, to numerically assess the effectiveness of the preparation scheme. Our proposal only utilizes existing experimental capabilities.The two-dimensional Bose-Hubbard model is one of the simplest many body systems that exhibits nontrivial physics. Initially proposed as a model for the superconductor insulator transition in solid state system [1,2], it was later realized most cleanly in optical lattices of ultracold atoms [3,4]. It has been widely studied by varying the ratio of hopping to interaction strength t/U , and the filling n b of bosons per site, which reveals the superfluid and Mott insulator phases and the quantum phase transition between them. A third natural parameter is the magnetic flux n φ , tuning of which has been demonstrated recently in ultra-cold atomic systems in periodically driven optical lattices [5][6][7][8]. The phase diagram as a function of magnetic flux through the unit cell is less understood. This is the bosonic analog of the HarperHofstadter problem of free electrons in a tight binding model with magnetic flux [9]. However, the bosonic problem is necessarily interacting and consequently allows for a richer variety of phases (also see related study of fractional Chern insulator [10][11][12][13][14]).At finite flux density, quantum Hall phases [15][16][17] of bosons might appear if the filling factor n b /n φ is appropriate. In the continuum limit U ∼ n φ 1 where the physics of LL applies, it was established numerically (e.g. see a review [18]) and analytically [19,20] that quantum Hall states appear. Many of those quantum Hall phases can be understood simply using Jain's composite fermion approach [21]. For example, one can first attach one flux quanta to the boson, converting them into composite fermions, and letting them form a ν CF = p integer quantum Hall state. This con...