Resonating Plaquette Phase of a Quantum Six-Vertex Model

Abstract

The simplest quantum generalization of the six-vertex model describes fluctuations of the order parameter of the d-density wave (DDW), believed to compete with superconductivity in the highTc superconductors. The ground state of this model undergoes a first order transition from the DDW phase to a resonating plaquette phase as the quantum fluctuations are increased, which is explored with the help of quantum Monte Carlo simulations and analytic considerations involving the n-vector (n = 2) model with cubic anisotropy. In addition to finding a new quantum state, we show that the DDW is robust against a class of quantum fluctuations of its order parameter. The inferred finite temperature phase diagram contains unsuspected multicritical points.PACS numbers: 71.10.Hf, 74.10.+v The vertex models have unusual building blocks: arrows joined at a site forming the vertex. Nonetheless the statistical mechanics of these models are well defined, elegant, and have unexpected connections to more intuitively familiar models. For example, the transfer matrix of the classical six-vertex model is the XXZHamiltonian [1] of Heisenberg spins and the corresponding transfer matrix of the eight vertex model is the XYZHamiltonian.[2] Both of these models are solved by powerful mathematical methods with far reaching consequences. These vertex models are not simply products of mathematical imagination but were originally proposed to describe phases of ferro and antiferroelectric materials.[3] Thus they are effective descriptions of complex organization of matter. These vertex models are classical because they are made out of commuting variables.The interest in the quantum six-vertex model, to be defined below, is rooted in the unusual phenomenology of the cuprate high temperature superconductors.[4] It has been argued that the origin of the pseudogap is an unconventional broken symmetry in which a particle and a hole is bound in an angular momentum l = 2 state, resulting in an order parameter, the d-density wave (DDW), which is effectively hidden.[5] The statistical mechanical description of DDW, which includes both thermal and quantum fluctuations of the directions of the bond currents, is the quantum six-vertex model. [4] In particular, the description of DDW in terms of the six-vertex model resolves the puzzle as to why there are no associated specific heat anomalies, as the phase transition corresponds to an essential singularity in the free energy. In this Letter we consider commensurate DDW as possible incommensuration wave vectors tend to be small in extended Hubbard models. [6] Among the observed broken symmetries in the particleparticle channel are s, p, and d-wave superconductors, where the Cooper pairs bind in the angular momentum channels l = 0, 1, and 2 respectively. It is remarkable however, that in the particle-hole channel, the observed broken symmetries are mainly confined to s-wave symmetry: s-wave singlet and triplet density waves, known as the charge and spin density waves respectively. [7] Here we investigate, for...

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice

“…It might also be interesting to revisit two-dimensional ice-type materials, such as the proton bonded ferroelectric copper formate tetrahydrate 41 . While two-dimensional quantum ice models are known to order at low temperatures [110][111][112][113][114][115] , they are described by the same class of lattice gauge theory, and possess the same spinon excitations as their three-dimensional counterparts 40,111,115 . These excitations will be confined in the ordered state, but might be visible at finite energy, and above the ordering temperature.…”

Correlated Fermions on a Checkerboard Lattice

“…In both cases, an effective gauge theory is a U(1) theory for such a critical point and a Z 2 theory for a deconfined phase [10,11]. Several related models, such as the quantum six/eight-vertex models [12,13,14,15] have been shown to conform to the same dichotomy: a model with orientable loops is critical and is described by a U(1) gauge theory.The aforementioned models share one important feature: the matrix elements connecting various states of the lowenergy Hilbert space are all non-negative. The Hilbert space separates into different sectors so that all states within a sector are connected by the quantum dynamics while states belonging to different sectors are not.…”

“…In both cases, an effective gauge theory is a U(1) theory for such a critical point and a Z 2 theory for a deconfined phase [10,11]. Several related models, such as the quantum six/eight-vertex models [12,13,14,15] have been shown to conform to the same dichotomy: a model with orientable loops is critical and is described by a U(1) gauge theory.…”

“…(3). The bosonic version studied in [13] has three phases depending on the parameter µ/g: the two "flat" phases, i.e., the Néel phase [13] and the plaquette phase (also found in [14,27]) as well as a maximally tilted frozen phase, with the RK point perched between the latter two phases. We have already argued that some of the flat states are actually frozen for fermions and hence cannot be used to define the fluctuationstabilized phases for µ/g < 1.…”

“…The different signs result from the number of permuted fermions which is either even or odd. Symmetries and Conserved Quantities -The first important point is that this model is a variation of the quantum sixvertex (6V) model [12,14,15] [29]. However, there are two important differences resulting from the fermionic statistics.…”