Universal Conductivity in a Two-Dimensional Superfluid-to-Insulator Quantum Critical System

Abstract

We compute the universal conductivity of the (2+1)-dimensional XY universality class, which is realized for a superfluid-to-Mott insulator quantum phase transition at constant density. Based on large-scale Monte Carlo simulations of the classical (2+1)-dimensional $J$-current model and the two-dimensional Bose-Hubbard model, we can precisely determine the conductivity on the quantum critical plateau, $\sigma (\infty )=0.359(4){\sigma }_Q$ with ${\sigma }_Q$ the conductivity quantum. The universal conductivity curve is the standard example with the lowest number of components where the bottoms-up AdS/CFT correspondence from string theory can be tested and made to use [R. C. Myers, S. Sachdev, and A. Singh, Phys. Rev. D83, 066017 (2011)]. For the first time, the shape of the $\sigma (i{\omega }_n)-\sigma (\infty )$ function in the Matsubara representation is accurate enough for a conclusive comparison and establishes the particle-like nature of charge transport. We find that the holographic gauge/gravity duality theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in a cold gas experiment are also determined by our calculation.

8 pages, 12 figures

References in corpus (5)

• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Monte Carlo study of two-dimensional Bose-Hubbard model
• The Higgs mode in a two-dimensional superfluid
• Dynamics and Conductivity Near Quantum Criticality
• Numerical study of duality and universality in a frozen superconductor

Cited by in corpus (47)

• Amplitude / Higgs Modes in Condensed Matter Physics
• Bootstrapping the O(N) Archipelago
• Two-terminal transport measurements with cold atoms
• The dynamics of quantum criticality via Quantum Monte Carlo and holography
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• DC resistivity at the onset of spin density wave order in two-dimensional metals
• Hydrodynamic transport in strongly coupled disordered quantum field theories
• High-harmonic generation approaching the quantum critical point of strongly correlated systems
• Scaling of disorder operator at deconfined quantum criticality
• Universal Features of Higher-Form Symmetries at Phase Transitions
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Optical conductivity of topological surface states with emergent supersymmetry
• Dynamical Conductivity Across The Disorder-Tuned Superconductor-Insulator Transition
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Quantum critical charge response from higher derivatives: is more different?
• Competing phases, phase separation and co-existence in the extended one-dimensional bosonic Hubbard model
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition
• An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$
• Fractionalized conductivity and emergent self-duality near topological phase transitions
• Dynamical response near quantum critical points
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Metal-Insulator Transition with Charge Fractionalization
• Extraordinary-log Universality of Critical Phenomena in Plane Defects
• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Holographic response from higher derivatives with homogeneous disorder
• A Holographic Model for Quantum Critical Responses
• Holographic quantum critical conductivity from higher derivative electrodynamics
• Taking a critical look at holographic critical matter
• Superuniversal transport near a $(2+1)$-dimensional quantum critical point
• Disorder Influences the Quantum Critical Transport at a Superconductor to Insulator Transition
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
• Critical behavior of the Higgs- and Goldstone-mass gaps for the two-dimensional S=1 XY model
• Demystifying the Holographic Mystique
• The halon: a quasiparticle featuring critical charge fractionalization
• Non-local correlation and entanglement of ultracold bosons in the two-dimensional Bose-Hubbard lattice at finite temperature
• Holographic study of shear viscosity and butterfly velocity for magnetic field-driven quantum criticality
• Conductivity of lattice bosons at high temperatures
• Momentum dissipation and holographic transport without self-duality
• Quantitative Studies on the Quantum Critical Regime near Superfluid to Mott Insulator Transition
• "Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator
• Graphical Representations and Worm Algorithms for the O($N$) Spin Model
• Even-Odd effect of an Spin-S impurity coupled to a quantum critical system
• Divergence of Dynamical Conductivity at Certain Percolative Superconductor-Insulator Transitions