Session H5: Frustrated Magnetism: Spin Liquids in 2D

Paired states of Chern-Simons fermions in quantum spin models

We consider exotic states constructed from the two-dimensional quantum spin-1/2 XY model on the square and hexagonal lattices. By applying a Chern-Simons transformation we represent the quantum spin model as a system of spinless fermions interacting via attached fluxes. The interaction is then decoupled in the Cooper and excitonic channels giving possible unconventional states of Chern-Simons fermions. We examine the mean field properties of these states and their relations to the original spin model.   

Symmetry fractionalization of visons in Z2 spin liquids

In this work we study symmetry fractionalization of vison excitations in topological $\mathbb{Z}_2$ spin liquids. We show that in the presence of the full $\mathrm{SO}(3)$ spin-rotational symmetry and if there is an odd number of spin-$\frac12$ per unit cell, the symmetry fractionalization of visons is completely fixed. On the other hand, visons can have different classes of symmetry fractionalization if the spin-rotational symmetry is reduced. As a concrete example, we show that visons in the Balents-Fisher-Girvin $\mathbb{Z}_2$ spin liquid have crystal symmetry fractionalization classes which are not allowed in $\mathrm{SO}(3)$ symmetric spin liquids, due to the reduced spin-rotational symmetry.   

Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid

Motivated by recent experimental realizations of artificial gauge fields in ultracold atoms, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-$1/2$ fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations.   

Unification of bosonic and fermionic $\mathbb{Z}_2$ spin liquids on a rectangular lattice

Recent theories [1] have postulated the presence of a fractionalized Fermi liquid ($FL^{*}$) in the pseudogap metal phase of cuprates. The $FL^{*}$ phase can be described as a spin liquid co-existing with fermionic charge carrying quasiparticles. Underdoped cuprates also show a variety of competing orders, including nematic order which reduce the $C_4$ symmetry of the square lattice to $C_2$. Motivated by this, we classify mean-field bosonic spin liquids on a rectangular lattice using projective symmetry groups (PSG) [2], and find equivalent descriptions in terms of fermionic partons [3]. In particular, we find a fermionic spin liquid ansatz corresponding to a bosonic $\mathbb{Z}_2$ spin liquid with favorable mean field energy [4]. The fermionic ansatz might be useful to investigate the transition from a $FL^{*}$ to a fermi liquid. [1]. Density-wave instabilities of fractionalized Fermi liquids: D. Chowdhury and S. Sachdev, PRB 90, 245136 (2014) [2] Quantum orders and symmetric spin liquids: XG Wen, PRB 65 (16), 165113 (2002) [3] Unification of bosonic and fermionic theories of spin liquids on the kagome lattice: Y-M. Lu, G. Y. Cho, A. Vishwanath, arXiv:1403.0575 [4] Large-N expansion for frustrated quantum antiferromagnets: N. Read and S. Sachdev, PRL 66, 1773 (1991)   

Coupled wire construction of chiral spin liquids

We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap, and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level k with parafermionic edge states.   

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

We investigate the Heisenberg model with chiral coupling on the triangular lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. As the chiral coupling grows, a gapped spin liquid with non-trivial magnetic fluxes and nonzero chiral order is stabilized. Furthermore, we calculate the topological Chern number and the degeneracy of the ground state, both of which lead us to identify this flux state as the chiral spin liquid with $C=1/2$ fractionalized Chern number. Finally, we add spatial anisotropy in the model to study the effects for the chiral order.   

Valence-bond-solid domain walls in a 2D quantum magnet

sing quantum Monte Carlo simulations, we study properties of domain walls in a square-lattice S=1/2 Heisenberg model with additional interactions which can drive the system from an antiferromagnetic (AFM) ground state to a valence-bond solid (VBS). We study the finite-size scaling of the domain-wall energy at the putative "deconfined" critical AFM-VBS point, which gives access to the critical exponent governing the domain-wall width. This length-scale diverges faster than the correlation length and also is related to the scale of spinon deconfinement. Our results show additional evidence of deconfied quantum criticality and are compatible with critical exponents extracted from finite-size scaling of other quantities.   

Field-induced magnetization jumps and quantum criticality in the 2D J-Q model

The J-Q model is a `designer hamiltonian' formed by adding a four spin `Q' term to the standard antiferromagnetic $S=1/2$ Heisenberg model. The Q term drives a quantum phase transition to a valence-bond solid (VBS) state: a non-magnetic state with a pattern of local singlets which breaks lattice symmetries. The elementary excitations of the VBS are triplons, i.e. gapped S=1 quasiparticles. There is considerable interest in the quantum phase transition between the N\'{e}el and VBS states as an example of deconfined quantum criticality. Near the phase boundary, triplons deconfine into pairs of bosonic spin-1/2 excitations known as spinons. Using exact diagonalization and the stochastic series expansion quantum monte carlo method, we study the 2D J-Q model in the presence of an external magnetic field. We use the field to force a nonzero density of magnetic excitations at T=0 and look for signatures of Bose-Einstein condensation of spinons. At higher magnetic fields, there is a jump in the induced magnetization caused by the onset of an effective attractive interaction between magnons on a ferromagnetic background. We characterize the first order quantum phase transition and determine the minimum value of the coupling ratio $q \equiv Q/J$ required to produce this jump.   

Chiral phase of a simple two-dimensional spin-1 quantum magnet

We investigate the evolution of the ground state of a simple spin-1 antiferromagnet with easy-axis single-ion anisotropy $D (S^z)^2$, with $D < 0$, on a two-dimensional triangular lattice. The ground state changes from a quantum paramagnet one, at sufficiently large $|D|$, to a magnetically ordered $120^\circ$ one at small $D\sim 0$. Besides breaking the continuous $U(1)$ symmetry of global spin rotations along the $z$-axis, this non-collinear ordering also breaks the discrete $Z_2$ {\em chiral} symmetry, which raises the possibility of an intermediate chiral spin liquid state, spontaneously breaking spatial inversion and mirror symmetries. We show that this interesting novel state indeed appears as a result of the condensation of bound $\langle S^+_n S^-_m- S^-_n S^+_m\rangle$ pairs. The resulting Ising-like nematic state supports a regular pattern of spin currents on the bonds of the triangular lattice. It represents quantum analogue of the classical chiral spin liquid proposed by Villain in 1977.   

Critical scaling corrections in 2D dimerized antiferromagnets

2D dimerized antiferromagnets can be driven through a quantum-critical point by tuning the ratio $g = J2/J1$ between inter- and intra-dimer couplings. It has been shown [1] that the systems fall into two classes, depending on whether or not a certain bond-inversion symmetry is present in the dimer pattern. The two classes should have the same leading critical exponents but different expo- nents controlling the scaling corrections. We here investigate the scaling correc- tions using quantum Monte Carlo simulations for several different dimerization patterns. We will discuss systematic methods to extract the scaling corrections in the thermodynamic limit. \bibitem{try} [1]L. Fritz, R. L. Doretto, S. Wessel, S. Wenzel, S. Burdin, and M. Vojta, Phys. Rev. B 83, 174416 (2011).   

Novel spin liquid with a gapped Fermi surface in the kagome Kondo-lattice model

Geometrical frustration in the Kagome lattice is well known as a source of many exotic phases. Here we study the under-screened Kondo-lattice model (KLM) on the kagome lattice at large electron-spin coupling, a regime in which perturbative approaches such as RKKY are invalid. We employ a recently developed linear-scaling, dynamical sampling method to study the KLM on large kagome lattices. At low temperatures, our simulations uncover an intriguing classical spin liquid phase with short-range correlations. Surprisingly, when $T \to 0$ a wide gap in the electronic spectrum can appear at any filling fraction between $0.5$ to $0.63$. We characterize this new spin liquid and discuss the origin of spontaneous gap formation.   

A tensor product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality

We study this model using the cluster update algorithm for tensor product states (TPSs). We find that the ground state energies at finite sizes and in the thermodynamic limit are in good agreement with the exact diagonalization study. At the largest bond dimension available $D=9$ and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point $J_2^{c_1}=0.53(1)J_1$ and the critical exponents $\beta=0.50(4)$. In the intermediate region we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation. By fitting a universal scaling function for the spin-spin correlation we find the critical exponents $\nu=0.68(3)$ and $\eta_s=0.34(6)$, which is very close to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at $J_2^{c_1}=0.53(1)J_1$.   

Magnetic fluctuations and dynamics in the vicinity of quantum spin liquids: Cluster dynamical mean-field study of the Kitaev model

The quantum spin liquid, which does not show any long-range ordering down to the lowest temperature, has attracted broad interest as a new quantum state of matter. Since the ground state of the Kitaev model was shown to be a quantum spin liquid in two dimensions [1], there has been an explosion in both theoretical and experimental studies. Nevertheless, dynamical properties at finite temperatures remain a challenge, despite the relevance to analysis of recent experiments for Ir and Ru compounds. In this contribution, we address this problem by using the cluster dynamical mean-field approximation, which we newly develop on the basis of the Majorana fermion representation. Using the continuous-time quantum Monte Carlo method for the impurity solver, we calculate the magnetic susceptibility, dynamical spin structure factor, and relaxation time in the nuclear magnetic resonance. We find that these quantities show peculiar temperature dependences in the paramagnetic state when approaching the quantum spin liquid by decreasing temperature, which reflects the fractionalization of quantum spins. We will discuss the results while changing the anisotropy and sign (ferro/antiferro) of the exchange interactions, in comparison with experiments. [1] A. Kitaev, Ann. Phys. {\bf 321}, 2 (2006).   

Protection against a spin gap in two-dimensional insulating antiferromagnets with a Chern-Simons term

We propose a mechanism for the protection against spin gapped states in doped antiferromagnets. It requires the presence of a Chern-Simons term that can be generated by a coupling between spin and an insulator.We first demonstrate that in the presence of this term the vortex loop excitations of the spin sector behave as anyons with fractional statistics. To generate such a term, the fermions should have a massive Dirac spectrum coupled to the emergent spin field of the spin sector. The Dirac spectrum can be realized by a planar spin configuration arising as the lowest-energy configuration of a square lattice antiferromagnet Hamiltonian involving a Dzyaloshinskii- Moriya interaction. The mass is provided by a combination of dimerization and staggered chemical potential.We finally showthat for realistic parameters, anyonic vortex loop condensationwill likely never occur and thus the spin gapped state is prevented.We also propose real magnetic materials for an experimental verification of our theory. Reference: Imam Makhfudz and Pierre Pujol,Phys.Rev. B 92, 144507(2015).   

Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling

There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While the on-going progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wavefunction or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase emerging in an extended Bose-Hubbard model on kagome lattice, where the non-interacting band structure is topological trivial with zero Berry curvature in the Brillouin zone. By means of an unbiased state-of-the-art density-matrix renormalization group technique, we identify that the groundstate in a broad parameter region is equivalent to a bosonic fractional quantum Hall Laughlin state, based on the characterization of unverisal properties including groundstate degeneracy, edge excitations and anyonic quasiparticle statistics. Our work paves a way of finding interaction induced topological phase at the phase boundary of conventionally ordered solid phases.