Transition from the Z2 spin liquid to antiferromagnetic order: Spectrum on the torus

We describe the finite-size spectrum in the vicinity of the quantum critical point between a Z2 spin liquid and a coplanar antiferromagnet on the torus. We obtain the universal evolution of all low-lying states in an antiferromagnet with global SU(2) spin rotation symmetry, as it moves from the 4-fold topological degeneracy in a gapped Z2 spin liquid to the Anderson “tower-of-states” in the ordered antiferromagnet. Due to the existence of nontrivial order on either side of this transition, this critical point cannot be described in a conventional Landau-Ginzburg-Wilson framework. Instead it is described by a theory involving fractionalized degrees of freedom known as the O(4)∗ model, whose spectrum is altered in a significant way by its proximity to a topologically ordered phase. We compute the spectrum by relating it to the spectrum of the O(4) Wilson-Fisher fixed point on the torus, modified with a selection rule on the states, and with nontrivial boundary conditions corresponding to topological sectors in the spin liquid. The spectrum of the critical O(2N) model is calculated directly at N = ∞, which then allows a reconstruction of the full spectrum of the O(2N)∗ model at leading order in 1/N. This spectrum is a unique characteristic of the vicinity of a fractionalized quantum critical point, as well as a universal signature of the existence of proximate Z2 topological and antiferromagnetically-ordered phases, and can be compared with numerical computations on quantum antiferromagnets on two dimensional lattices.Physic

Real-time dynamics of string breaking in quantum spin chains

String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process: First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated time scale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.Comment: 16 pages, 8 figures; version published in Physical Review

Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point

We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled {\em chiral Ising} fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with ${n_\text{D}=4}$ component Dirac spinors in $D=(2+1)$ dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or $\pi$-flux square lattice. The torus spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus spectrum analytically using the perturbative expansion in ${\epsilon = 4 - D}$, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical torus spectrum. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.Comment: 24 pages, 14 figure

Frustration-induced anomalous transport and strong photon decay in waveguide QED

We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the "dressed-spin", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at higher energies. We also show that the photons can decay into multiple photons of smaller energies. The total probability of these inelastic processes can be as large as the total elastic scattering rate, or half of the total scattering rate, which is as large as it can be. The frustrated spin induces strong anisotropic photon-photon interactions that are dominated by inter-species interactions. Our results are relevant to state-of-the-art circuit and cavity quantum electrodynamics experiments.Comment: 5+13 pages, 3 + 6 figures. v2: changed title and presentatio

Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.Comment: 9 pages, 9 figure

Renormalization group analysis of a fermionic hot-spot model

We present a renormalization group (RG) analysis of a fermionic “hot-spot” model of interacting electrons on the square lattice. We truncate the Fermi-surface excitations to linearly dispersing quasiparticles in the vicinity of eight hot spots on the Fermi surface, with each hot spot separated from another by the wave vector (π,π). This is motivated by the importance of these Fermi-surface locations to the onset of antiferromagnetic order; however, we allow for all possible quartic interactions between the fermions, and also for all possible ordering instabilities. We compute the RG equations for our model, which depend on whether or not the hot spots are perfectly nested, and relate our results to earlier models. We also compute the RG flow of the relevant order parameters for both Hubbard and J,V interactions, and present our results for the dominant instabilities in the nested and non-nested cases. In particular, we find that non-nested hot spots with J,V interactions have competing singlet dx2−y2 superconducting and d-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wave vectors, and find dominant d-form factor enhancement for a range of couplings.Physic