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Register a new userConstructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
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We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated to the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.
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We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.
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.
We study the robustness of the paradigmatic kagome Resonating Valence Bond (RVB) spin liquid and its orthogonal version, the quantum dimer model. The non-orthogonality of singlets in the RVB model and the induced finite length scale not only makes it difficult to analyze, but can also significantly affect its physics, such as how much noise resilience it exhibits. Surprisingly, we find that this is not the case: The amount of perturbations which the RVB spin liquid can tolerate is not affected by the finite correlation length, making the dimer model a viable model for studying RVB physics under perturbations. Remarkably, we find that this is a universal phenomenon protected by symmetries: First, the dominant correlations in the RVB are spinon correlations, making the state robust against doping with visons. Second, reflection symmetry stabilizes the spin liquid against doping with spinons, by forbidding mixing of the initially dominant correlations with those which lead to the breakdown of topological order.
Symmetry-protected trivial (SPt) phases of matter are the product-state analogue of symmetry-protected topological (SPT) phases. This means, SPt phases can be adiabatically connected to a product state by some path that preserves the protecting symmetry. Moreover, SPt and SPT phases can be adiabatically connected to each other when interaction terms that break the symmetries protecting the SPT order are added in the Hamiltonian. It is also known that spin-1 SPT phases in quantum spin chains can emerge as effective intermediate phases of spin-2 Hamiltonians. In this paper we show that a similar scenario is also valid for SPt phases. More precisely, we show that for a given spin-2 quantum chain, effective intermediate spin-1 SPt phases emerge in some regions of the phase diagram, these also being adiabatically connected to non-trivial intermediate SPT phases. We characterize the phase diagram of our model by studying quantities such as the entanglement entropy, symmetry-related order parameters, and 1-site fidelities. Our numerical analysis uses Matrix Product States (MPS) and the infinite Time-Evolving Block Decimation (iTEBD) method to approximate ground states of the system in the thermodynamic limit. Moreover, we provide a field theory description of the possible quantum phase transitions between the SPt phases. Together with the numerical results, such a description shows that the transitions may be described by Conformal Field Theories (CFT) with central charge c=1. Our results are in agreement, and further generalize, those in [Y. Fuji, F. Pollmann, M. Oshikawa, Phys. Rev. Lett. 114, 177204 (2015)].
We present a general review of the projective symmetry group classification of fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then introduce a systematic generalization of the approach for symmetric $mathbb{Z}_2$ quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral $mathbb{Z}_2$ states, we study the subset of U(1) phases variationally in the antiferromagnetic $J_1$-$J_2$-$J_d$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.
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