Session G50: Quantum Criticality Theory

Quantum Criticality of Semi-Dirac Fermions

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions toward charge and spin density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell renormalization group. We generalize to a large number of fermion flavors, N, to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including universal 1/N corrections. The anomalous dimension of the fermion fields vanishes in the large N limit, consistent with a recovery of Fermi-liquid behaviour. However, many other unusual features persist. We show that this is a consequence of non-analytic terms in the mean-field free energy of semi-Dirac fermions.   

Quantum Criticality of Multiband Polar Metals

Quantum criticality in metallic systems leads to a variety of exotic behaviors, that sensitively depend on the type of the transition. The case of a polar transition in a metal, structurally identical to a ferroelectric transition in an insulator, has received attention recently due to the discovery of a number of metallic compounds where a polar order exists.

We show that quantum criticality of multiband polar metals is of particular interest, as a strong coupling of the charge carriers to the critical mode can be realized near the band crossings in momentum space. We provide a comprehensive classification of the possible emerging quantum critical behaviors and find evidence for strong interaction effects and, in some cases, non-Fermi liquid physics. The critical properties are found to depend on the type of band crossing as well as dimensionality. Experiments, that can allow to probe the emergent behavior, and implications for existing materials are discussed.   

Deconfined quantum criticality in the 2D J-Q model

The deconfined quantum critical point (DQCP) was proposed as a new scenario for quantum phase transitions fifteen years ago [1] and is still an enigmatic concept, with no general consensus on its existence. To test the DQCP proposal, which is based on a quantum field theory that cannot be solved, numerical studies of various lattice models have been considered. While no direct signs of discontinuities have been observed in the finite-size scaling, there are scaling anomalies that have led to speculations of a weak first-order transition described by a non-unitary conformal field theory [2]. Another possibility is that the transition is continuous but violates standard scaling laws. The observed finite-size scaling violations can be described phenomenologically by a scaling form with two relevant fields that are tuned by the same parameter in the Hamiltonian [3]. We will discuss recent work aimed at high-precision tests of this type of scaling by doing large scale calculation of the J-Q model which can realize the quantum phase transition between the antiferromagnetic state and a valence-bond solid state.

[1] Science 303, 1490 (2004).
[2] Phys. Rev. X 7, 031051 (2017).
[3] Science 352, 213 (2016).   

Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids

We show that the ballistic regime in two-dimensional Fermi liquids is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a free conformal field theory (CFT) with a dynamical scaling exponent z = 1. Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has vortices at all spatial scales. The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. We animate the emergence of critical spatial (vimeo.com/365020115) and Fermi surface (vimeo.com/364982637) fluctuations as experimental parameters are tuned to the QCP. The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics (vimeo.com/366725650).   

Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point

We study the stability of the Wilson-Fisher fixed point of the quantum O(2N) vector model to quenched disorder in the large-N limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the strong interactions of the Wilson-Fisher fixed point. This enables a perturbative renormalization group study of the interplay of disorder and interactions about this fixed point. We show that, in contrast to the spiralling flows obtained in earlier double-ε expansions, the theory flows directly to a quantum critical point characterized by finite disorder and interactions. The critical exponents we obtain for this transition are in remarkable agreement with numerical studies of the superfluid-Mott glass transition. We additionally discuss the stability of this fixed point to scalar and vector potential disorder and use proposed boson-fermion dualities to make conjectures regarding the effects of weak disorder on dual Abelian Higgs and Chern-Simons-Dirac fermion theories when N=1.   

Deconfined quantum critical point in the extended Hubbard model: a sign-problem-free quantum Monte Carlo study

Deconfined quantum critical point (DQCP) describes a type of quantum phase transitions at T=0 beyond Landau paradigm, where a continuous transition appears between ordered phases with incompatible broken symmetries. Convincing evidences of DQCP in correlated fermionic systems are scarce. Here we study the quantum phase diagram and phase transition on an extended Hubbard model of fermions on the square lattice. By performing determinant quantum Monte Carlo simulation, we establish the ground-state phase diagram of this model, and more intriguingly, show convincing evidence of a continuous phase transition between valence-bond-solid (VBS) and antiferromagnetic (AF) phases when the interaction strength is varied. We believe that our study provides a novel platform for the investigation of DQCP in the strongly correlated fermionic systems.   

Deconfined quantum criticality and emergent SO(5) symmetry in fermionic systems

Deconfined quantum criticality with emergent SO(5) symmetry in correlated systems remains elusive. Here, by performing numerically-exact state-of-the-art quantum Monte Carlo (QMC) simulations, we show convincing evidences of deconfined quantum critical points (DQCP) between antiferromagnetic and valence-bond-solid phases in the extended Hubbard model of fermions on the honeycomb lattice with large system sizes. We further demonstrate evidences of the SO(5) symmetry at the DQCP. Moreover, it is the first time that the critical exponents obtained at the DQCP are consistent with the rigourous conformal bounds. Consequently, we establish a promising arena of DQCP with emergent SO(5) symmetry in interacting systems of fermions. Its possible experimental relevances in correlated systems such as graphene-family materials will be discussed briefly [1].
[1] Zi-Xiang Li, Shao-Kai Jian, and Hong Yao, arXiv:1904.10975   

Exploring a quantum critical point in the 3D Hubbard model using the dynamical cluster approximation

This research simulates the single band three dimensional Hubbard Model using the dynamical cluster approximation. Away from half-filling the system appears to undergo a quantum phase transition driven by the chemical potential or doping level. The quasiparticle weight, extracted from the self-energy, is used to identify the emergence of a Fermi liquid phase. At lower fillings the quasiparticle weight maintains a finite value consistent with a Fermi liquid state. Nearer to half-filling the quasiparticle weight tends towards zero suggesting a non-Fermi liquid state. We also search for evidence of a marginal Fermi liquid state, a signature of the quantum criticality. In order to complete this simulation efficiently the continuous time quantum Monte Carlo method is run on a massively parallel simulation.   

Many-body chaos in the antiferromagnetic quantum critical metal

Recently, the scrambling rate as defined from the exponential growth of regularized out-of-time-ordered correlators has been used as a measure of integrability in quantum many-body systems. We compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory of Phys. Rev. X 7, 021010 (2017). At this strongly coupled fixed point, there is an emergent small control parameter w that is a ratio of natural parameters of the theory. The strong coupling is unequally felt by the two degrees of freedom: the bosonic AFM collective mode is heavily dressed by interactions with the electrons, while the electron is only marginally renormalized. The scrambling rates of both degrees of freedom are linear in temperature (up to logarithms), but come with very different powers of w, indicating the different "degrees of integrability" of the two sectors of the theory. Although the interaction strength is of order unity, the larger Lyapunov exponent is still parametrically smaller than the universal upper bound. We also show that due to the non-local nature of the boson propagator, its effective "butterfly velocity" of the chaos front is infinite.   

Monopole hierarchy at a quantum critical point between a Dirac spin liquid and an antiferromagnet

Certain frustrated 2D quantum magnets may be described at low energy by a Dirac spin liquid (DSL) which is a version of quantum electrodynamics with 2N flavors of two-component gapless Dirac spinons. A DSL also hosts monopole excitations due to the compactness of the emergent U(1) gauge field. These drive the confinement of the spinons. We revisit the hierarchy among monopole operators with different quantum numbers at the quantum critical point (QCP) between a DSL and an antiferromagnet. By obtaining the scaling dimension of monopole operators while constraining their spin quantum number, we explicitly show their organization into multiplets of the QCP flavor symmetry group SU(2)xSU(N). We also discuss 1/N corrections to the scaling dimension of monopoles at a critical point between a DSL and a chiral spin liquid.   

The Hall Effect and Dynamical Scaling about the Quantum Critical Point in Elemental Chromium

Elemental chromium is a spin-density-wave (SDW) antiferromagnet that can be tuned through a second order quantum phase transition by the application of 10 GPa of pressure. A nesting condition in the paramagnetic Fermi surface partially gaps the Fermi surface and forms the SDW. Since the Hall coefficient directly probes properties of the Fermi surface, it is an effective tool to investigate the evolution of the Fermi surface in the quantum critical regime, where there are indications of strong-coupling physics. In the low temperature limit, the Hall coefficient varies rapidly with pressure across the quantum critical point. By extending this measurement to higher temperatures, we are able to track the P-T dependence of this crossover and test analogies to the pseudogap phase in the superconducting cuprates. The temperature dependence of the width of this crossover constrains theories of dynamical scaling at the quantum critical point.   

Optical Conductivity of the Two Dimensional Anti-ferromagnetic Quantum Critical Metal

In the two-dimensional anti-ferromagnetic quantum critical metal, coherent quasi-particle(s) ceases to exist at the hot spots due to strong coupling with soft spin fluctuations. Over an intermediate energy scale, physical responses of the non-Fermi liquid is controlled by the nesting angle between patches of Fermi surface connected by the anti-ferromagnetic wave-vector. For instance, the anomalous dimension of electron(s) at the hot spots defined over an intermediate energy scale decreases with decreasing nesting angle due to an increased damping of spin fluctuations by particle-hole excitation. In this work, we compute the optical conductivity of the non-Fermi liquid state as a function of the nesting angle. Remarkably, the weight of the conductivity that scales anomalously with frequency due to the soft spin fluctuations is enhanced as the nesting angle decreases. This is attributed to the fact that the increased number of electrons that are subject to scattering with spin fluctuations overcompensates the decreased scattering rate of individual electrons.   

Quantum criticalities with lattice vibrations

Quantum criticality is one of the most important concepts in modern condensed matter physics, as novel physics may arise in the vicinity of the quantum critical point by quantum fluctuations. These fluctuations inevitably couple to lattice vibrations in real materials due to the lattice structures. It is well understood that a class of thermal continuous transitions on lattices is eventually destabilized by either macroscopic instability of lattice structures or induced first-order symmetry breaking transitions. However, for the quantum phase transition, little is known about its consequences. Here, we demonstrate that such interplay between quantum criticality and lattice vibration leads to a new class of quantum many-particle phenomena. Moreover, we suggest a new stability condition for these criticalities which generalizes the specific-heat criterion of thermal transitions to a quantum version. Our results suggest a new direction to find novel quantum criticalities in nature.   

Novel Criticality of Dirac Fermions from Lattice Symmetry Breaking

We consider the role of spontaneous lattice symmetry breaking in strongly interacting two dimensional Dirac systems. The fermion induced quantum (multi-)criticality is described by Dirac fermions coupled to a dynamical order parameter that is composed of mass and emergent gauge fields. This is illustrated for the example of translational symmetry breaking due to charge-density wave order on the honeycomb lattice. Using a renormalization-group analysis we find that the putative emergent Lorentz invariance is violated. Finally, we identify that topological phase transitions are well described by this effective field theory.   

Kardar-Parisi-Zhang universality from soft gauge modes

The emergence of superdiffusive spin dynamics in integrable classical and quantum magnets is well established by now, but there is no generally valid theoretical explanation for this phenomenon. A fundamental difficulty is that the hydrodynamic fluctuations of conserved quasiparticle modes are purely diffusive. We propose a "hydrodynamic Higgs mechanism" in isotropic integrable magnets, which generates soft gauge modes that are decoupled from the quasiparticle sector. We show that the coarse-grained time evolution of these modes lies in the Kardar-Parisi-Zhang universality class of dynamics.