We construct a broad class of frustration-free quantum vertex models in 3+1D whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold for general 3D lattices with even coordination number. The corresponding classical vertex models have a $\mathbb{Z}_2$ gauge constraint enriched with a $\mathbb{Z}_2$ global symmetry. We study the interplay between these symmetries by exploiting exact wavefunction dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of $U(1)$ quantum spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the $\mathbb{Z}_2$ deconfined and $\mathbb{Z}_2$ symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.
It is generally accepted that doped Mott insulators can be well characterized by the t-J model. In the t-J model, the electron fractionalization is dictated by the phase string effect. We found that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and {\it vice versa} in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters d…
The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in J_xy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order J^2_xy/J_z on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six--vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes - a phase with long range Neel order and confined spinon excitations, a non-magnetic state of resonating squa…
We investigate the divergences appearing in the two-particle irreducible vertex functions of many-fermion systems with attractive on-site interactions. By means of dynamical mean-field theory calculations, we determine the location of singularity lines in the phase diagram of the attractive Hubbard model at half-filling, where the local Bethe-Salpeter equations are non invertible. We find that divergences appear both in the magnetic and in the density scattering channels. The former affect a sector of suppressed fluctuations and comply with the mapping of the physical susceptibilities of the r…
Behavior of doped fermions in $Z_2$ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the $Z_2$ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically-ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the …
We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially under point-group operations, their point-group behavior in the band language can be simplified by choosing a suitable Bloch basis.We first give two analytically accessible examples. Then we show that, for a large class of models, a natural Bloch basis exists, in which the vertex functions in the band language transform trivially under all point-group operations…
The interplay of electronic correlations, spin-orbit coupling and topology holds promise for the realization of exotic states of quantum matter. Models of strongly interacting electrons on honeycomb lattices have revealed rich phase diagrams featuring unconventional quantum states including chiral superconductivity and correlated quantum spin Hall insulators intertwining with complex magnetic order. Material realizations of these electronic states are however scarce or inexistent. In this work, we propose and show that stacking 1T-TaSe$_{2}$ into bilayers can deconfine electrons from a deep Mo…
We evaluate the dominant superconducting pairing symmetry in some 3-dimensional cubic lattice struct ures within the third-order perturbation theory with respect to the on-site coulomb repulsion. We cl arify whether the vertex correction term, which has a critical contribution to the p-wave state in t he 2-dimensional systems, is also important in the 3-dimensional system. We finally investigate the interplay between dimensionality and the vertex correction to grasp common features independent of t he lattice structures in the mechanism of the superconductivity.
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make an important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that -in contradiction to the conventional Hertz-Millis-Moriya theory- its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electro…
Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a 1/8 doped two-dimensional Hubbard model with imposed uni-directional stripe-like charge density wave modulation. We find a significant increase of the pairing correlations and critical temperature relative to the homogeneous system when the modulation length-scale is sufficiently large. With a separable form of the irreducible particle-particle vertex, we show that optimized superconductivity is obtained for moderate modulation strength due to a delicate balance between the modulation enhanced pai…
We investigate the charge- and spin dynamical structure factors for the 2D one-band Hubbard model in the strong coupling regime within an extension of the Dynamical Cluster Approximation (DCA) to two-particle response functions. The full irreducible two-particle vertex with three momenta and frequencies is approximated by an effective vertex dependent on the momentum and frequency of the spin/charge excitation. In the spirit of the DCA, the effective vertex is calculated with quantum Monte Carlo methods on a finite cluster. On the basis of a comparison with high temperature auxiliary field qua…
Ferromagnetism in the t-t' Hubbard model is investigated on a square lattice. Correlation effects in the form of self-energy and vertex corrections are systematically incorporated within a spin-rotationally-symmetric scheme which explicitly preserves the Goldstone mode and is therefore in accord with the Mermin-Wagner theorem. Interplay of band dispersion and correlation effects on ferromagnetic-state stability are highlighted with respect to both long- and short-wavelength fluctuations, which are shown to have substantially different behaviour. Our approach provides a novel understanding of t…
Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy ($1/{\cal N}$) expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the be…
Oddities in the Entanglement Scaling of the Quantum Six-Vertex Model
University of the Basque Country UPV/EHU（巴斯克大学）；DIPC - Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克拉巴斯克科学基金会）；European Organization for Nuclear Research (CERN)（欧洲核子研究组织（CERN））；Instituto de Física Teórica, UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）
We calculate using perturbative calculations and Ward identities the basic parameters of the Fermi Liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short ranged interaction at non-zero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard T=0 relationships for a Galilean-invariant Fermi Liquid are violated by finite-temperatu…
Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher's mapping of two dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagetic Ising model maps onto a non-symmetry breaking transition in dimer language -- instead it becomes a deconfinement transition for test monomers. Next, we introduce a modification of Fisher's mapping in which a second dimer model, also equivalent to the Ising model, is defined on a generically different lattice derived from the dual. In contrast to Fisher's original mappi…
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo si…
Understanding the nature of confinement, as well as its relation with the spontaneous breaking of chiral symmetry, remains one of the long-standing questions in high-energy physics. The difficulty of this task stems from the limitations of current analytical and numerical techniques to address non-perturbative phenomena in non-Abelian gauge theories. In this work, we show how similar phenomena emerge in simpler models, and how these can be further investigated using state-of-the-art cold-atom quantum simulators. More specifically, we introduce the rotor Jackiw-Rebbi model, a (1+1)-dimensional …
