FIG 10 - uploaded by Garry Goldstein
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Unit cell of the diamond lattice showing the lattice vectors e 1,...,4 introduced in the text. The two interpenetrating fcc lattices are shown as solid and open dots, respectively. A hexagonal plaquette is shown shaded by way of example.
Source publication
Some of the exciting phenomena uncovered in strongly correlated systems in recent years—for instance, quantum topological order, deconfined quantum criticality, and emergent gauge symmetries—appear in systems in which the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedo...
Citations
... For V > 0, g is expected to decrease with temperature T /|V | until g → 0, where the subleading terms (not included in Eq. 1) become important and could describe the transition to the non-flippable states [32][33][34]. We note that Eq. 1 can alternatively be obtained from a quantum treatment of a QDM field theory taken at finite temperature (see Ref. 35 and 36 for different approaches and for explicit expressions for the subleading terms), and was justified for the CIDM using rigorous arguments in Ref. 37. Based on the equivalence between quantum models at finite temperature and classical models, we expect that Eq. 1 describes the high-temperature phase of the QDM, including the transitions to the low-temperature ordered phases. In this work, we study by numerical means, using quantum Monte Carlo (QMC) techniques, the finitetemperature phase diagram of the QDM on the square lattice and verify this expectation, focusing in particular on the high-temperature critical phase parametrized by a g that depends non-trivially on both the temperature and the potential V . ...
We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows to implement exactly the dimer constraint, supplemented with a equal-time directed loop move that allows to sample winding sectors. We find a high-temperature critical phase with power-law correlations that extend down to the Rokshar-Kivelson point, in the vicinity of which a re-entrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-temperature transitions to ordered states (columnar and staggered) which match those of interacting classical dimer models.
... Our approach is not limited to quantum spin ice systems, and can be straightforwardly generalised to other QSLs underpinned by perturbative ring exchange processes, as well as to valence bond and quantum dimer models (e.g., following the route proposed in Ref. [44]). It will be also interesting to extend our work, for example to include additional terms in the Hamiltonian that may allow to change the relative strength of the vison bare cost and interactions, thus tuning the system between the weak and strong electrolyte limits; or more ambitiously, to include spinon excitations and study their interplay with photons and visons in QSI and QSLs in general. ...
... Beyond QSI, our approach is manifestly applicable to other quantum spin liquids underpinned by ring exchange processes. Quantum dimer models are a salient example, especially in light of novel large-S analytical approaches [44] and the fact that on non-bipartite lattices, they give rise to Z 2 RVB phases [22]. Our technique could add to the understanding of these phases, in particular the behaviour of the Z 2 vison excitations in the large-S limit, and their interplay with the dimer liquid background as correlations develop in the system, e.g., upon approaching quantum critical points out of the Z 2 RVB phase. ...
Understanding the nature and behaviour of excitations in quantum spin liquids, and in topological phases of matter in general, is of fundamental importance, and has proven crucial for experimental detection and characterisation of candidate materials. Current theoretical and numerical techniques, however, have limited capabilities, especially when it comes to studying gapped excitations. In this paper, we propose a semiclassical numerical method, based on large-$S$ path integral approach, to study systems whose spin liquid behaviour is underpinned by perturbative ring-exchange Hamiltonians. Our method can readily access both thermodynamic and spectral properties. We focus in particular on quantum spin ice and its photon and vison excitations. After benchmarking the method against existing results on photons, we use it to characterise visons and their thermodynamic behaviour, which remained hitherto largely unexplored. We find that visons form a weak electrolyte - in contrast to spinons in classical spin ice. That is, vison pairs are the dominant population at low temperatures. This is reflected in the behaviour of thermodynamic quantities, such as pinch point motifs in the relevant spin correlators. Visons also appear to strongly hybridise with the photon background, a phenomenon that gravely affects the way these quasiparticles may show up in inelastic response measurements. Our results demonstrate that the method, and generalisations thereof, can substantially help our understanding of quasiparticles and their interplay in quantum spin ice and other quantum spin liquids, quantum dimer models, and lattice gauge theories in general.
We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows the exact implementation of the dimer constraint, supplemented with an equal-time directed loop move that allows sampling the winding sectors. We find a high-temperature critical phase with power-law correlations that extends down to the Rokhsar-Kivelson point, in the vicinity of which a reentrance effect in the lines of constant exponent is found. For small values of the kinetic energy strength, we find finite-temperature transitions to ordered states (columnar and staggered) which match those of interacting classical dimer models.
