While gauge symmetry is a well-established requirement for representing topological orders in projected entangled-pair state (PEPS), its impact on the properties of low-lying excited states remains relatively unexplored. Here we perform PEPS simulations of low-energy dynamics in the Kitaev honeycomb model, which supports fractionalized gauge flux (vison) excitations. We identify gauge symmetry emerging upon optimizing an unbiased PEPS ground state. Using the PEPS adapted local mode approximation, we further classify the low-lying excited states by discerning different vison sectors. Our simulations of spin and spin-dimer dynamical correlations establish close connections with experimental observations. Notably, the selection rule imposed by the locally conserved visons results in nearly flat dispersions in momentum space for excited states belonging to the 2-vison or 4-vison sectors.

Continuer la lecture Partager

A harmonically trapped active Brownian particle exhibits two types of positional distributions—one has a single peak and the other has a single well—that signify steady-state dynamics with low and high activity, respectively. Adding inertia to the translational motion preserves this strict classification of either single-peak or single-well densities but shifts the dividing boundary between the states in the parameter space. We characterize this shift for the dynamics in one spatial dimension using the static Fokker-Planck equation for the full joint distribution of the state space. We derive local results analytically with a perturbation method for a small rotational velocity and then extend them globally with a numerical approach.

Continuer la lecture Partager

Using a high-accuracy variational Monte Carlo approach based on group-convolutional neural networks, we obtain the symmetry-resolved low-energy spectrum of the spin-1/2 Heisenberg model on several highly symmetric fullerene geometries, including the famous C60 buckminsterfullerene. We argue that as the degree of frustration is lowered in large fullerenes, they display characteristic features of incipient magnetic ordering: Correlation functions show high-intensity Bragg peaks consistent with Néel-like ordering, while the low-energy spectrum is organized into a tower of states. Competition with frustration, however, turns the simple Néel order into a noncoplanar one. Remarkably, we find and predict chiral incipient ordering in a large number of fullerene structures.

Continuer la lecture Partager

Quantum electrodynamics in <math display="inline"><mn>2</mn><mo>+</mo><mn>1</mn></math> dimensions (<math display="inline"><mrow><msub><mrow><mi>QED</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated <math display="inline"><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>1</mn></mrow></msub><mtext>-</mtext><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from <math display="inline"><mrow><msub><mrow><mi>QED</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>, in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of <math display="inline"><mrow><msub><mrow><mi>QED</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by <math display="inline"><mrow><msub><mrow><mi>QED</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to <math display="inline"><mi>N</mi><mo>=</mo><mn>48</mn></math> sites.

Continuer la lecture Partager