`We propose a general principle for constructing higher-order topological (HOT) phases. We argue that if a D -dimensional first-order or regular topological phase involves m Hermitian matrices that ...anticommute with additional p − 1 mutually anticommuting matrices, it is conceivable to realize an n th -order HOT phase, where n = 1 , ... , p , with appropriate combinations of discrete symmetry-breaking Wilsonian masses. An n th -order HOT phase accommodates zero modes on a surface with codimension n . We exemplify these scenarios for prototypical three-dimensional gapless systems, such as a nodal-loop semimetal possessing SU(2) spin-rotational symmetry, and Dirac semimetals, transforming under (pseudo)spin- 1/2 or 1 representations. The former system permits an unprecedented realization of a fourth-order phase, without any surface zero modes. Our construction can be generalized to HOT insulators and superconductors in any dimension and symmetry class.
Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant ...positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.
In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter ...regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry-an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.
The Jordan–Wigner transformation is a powerful tool for converting systems of spins into systems of fermions, or vice versa. While this mapping is exact, the transformation itself depends on the ...labelling of the spins. One consequence of this dependence is that approximate solutions of a Jordan–Wigner-transformed Hamiltonian may depend on the (physically inconsequential) labelling of the spins. In this work, we turn to an extended Jordan–Wigner transformation which remedies this problem and which may also introduce some correlation atop the Hartree–Fock solution of a transformed spin Hamiltonian. We demonstrate that this extended Jordan–Wigner transformation can be thought of as arising from a unitary version of the Lie algebraic similarity transformation (LAST) theory. Here, we show how these ideas, particularly in combination with the standard (non-unitary) version of LAST, can provide a potentially powerful tool for the treatment of the XXZ and J1–J2 Heisenberg Hamiltonians.
Over the past several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon ...modes and the on-site charge density. A quite different, and interesting, case is one in which the phonons live on the bonds, and hence modulate the electron hopping. This situation, described by the Su-Schrieffer-Heeger (SSH) Hamiltonian, has so far only been studied with quantum Monte Carlo in one dimension. Here we present results for the 2D SSH model, show that a bond ordered wave (BOW) insulator is present in the ground state at half filling, and argue that a critical value of the electron-phonon coupling is required for its onset, in contradistinction with the 1D case where BOW exists for any nonzero coupling. We determine the precise nature of the bond ordering pattern, which has hitherto been controversial, and the critical transition temperature, which is associated with a spontaneous breaking of Z_{4} symmetry.
This paper deals with the formulation, calibration, and validation of the Lattice Discrete Particle Model (LDPM) suitable for the simulation of the failure behavior of concrete. LDPM simulates ...concrete at the meso-scale considered to be the length scale of coarse aggregate pieces. LDPM is formulated in the framework of discrete models for which the unknown displacement field is not continuous but only defined at a finite number of points representing the center of aggregate particles. Size and distribution of the particles are obtained according to the actual aggregate size distribution of concrete. Discrete compatibility and equilibrium equations are used to formulate the governing equations of the LDPM computational framework. Particle contact behavior represents the mechanical interaction among adjacent aggregate particles through the embedding mortar. Such interaction is governed by meso-scale constitutive equations simulating meso-scale tensile fracturing with strain-softening, cohesive and frictional shearing, and nonlinear compressive behavior with strain-hardening. The present, Part I, of this two-part study deals with model formulation leaving model calibration and validation to the subsequent Part II.
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension d = 2 to 7 with periodic boundary conditions. The critical exponents associated to the finite-size ...scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension d = 4, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For d ≥ 5, the estimates of the exponents are close to the prediction d/2 when taking into account the dangerous irrelevant variable at the Gaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not dc = 6 as claimed in the literature, but dc = 4 like the equilibrium Ising model.
Spin q–Whittaker polynomials Borodin, Alexei; Wheeler, Michael
Advances in mathematics (New York. 1965),
01/2021, Letnik:
376
Journal Article
Recenzirano
Odprti dostop
We introduce and study a one-parameter generalization of the q–Whittaker symmetric functions. This is a family of multivariate symmetric polynomials, whose construction may be viewed as an ...application of the procedure of fusion from integrable lattice models to a vertex model interpretation of a one-parameter generalization of Hall–Littlewood polynomials from 3,6,7.
We prove branching and Pieri rules, standard and dual (skew) Cauchy summation identities, and an integral representation for the new polynomials.
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