arXiv subjects

Subir Sachdev

Publications and source records attributed to Subir Sachdev.

At least 217 records · Page 12Linked to original sources

arXiv2014

Multipoint correlators of conformal field theories: implications for quantum critical transport

We compute three-point correlators between the stress-energy tensor and conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an effective action on 3+1 dimensional anti-de Sitter space (AdS_4) proposed by Myers et al., and depend upon the co-efficient, γ, of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of γ. The CFTs of free fermions and bosons take the values γ=1/12,-1/12 respectively, and so saturate the bound |γ| <= 1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of γ. The value of γalso controls the frequency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of γlead to an appealing physical interpretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics.This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.

cond-mat.str-el↗

arXiv2014

Deconfined criticality in bilayer graphene

We propose that bilayer graphene can provide an experimental realization of deconfined criticality. Current experiments indicate the presence of Néel order in the presence of a moderate magnetic field. The Néel order can be destabilized by application of a transverse electric field. The resulting electric field induced state is likely to have valence bond solid order, and the transition can acquire the emergent fractionalized and gauge excitations of deconfined criticality.

cond-mat.str-el↗

arXiv2014

Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory

We describe the dynamics of a single fermion in a dispersionless band coupled to the 2+1 dimensional conformal field theory (CFT) describing the quantum phase transition of a bosonic order parameter with N components. The fermionic spectral functions are expected to apply to the vicinity of quantum critical points in two-dimensional metals over an intermediate temperature regime where the Landau damping of the order parameter can be neglected. Some of our results are obtained by a mapping to an auxiliary problem of a CFT containing a defect line with an external field which locally breaks the global O(N) symmetry.

cond-mat.str-el↗

arXiv2014

Quantum quenches and competing orders: I. Time-dependent Hartree-Fock+BCS theory

We study the non-equlibrium dynamics of an electronic model of competing bond density wave order and $d$-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, $(\boldsymbol{k}, -\boldsymbol{k})$, in the Brillouin zone. We compare the results of numerical studies of our model with recent picosecond optical experiments.

cond-mat.supr-con↗

arXiv2014

Quantum quenches and competing orders

We study the nonequilibrium dynamics of an electronic model of competition between an unconventional charge density wave (a bond density wave) and $d$-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, ( $\boldsymbol{k}$, - $\boldsymbol{k}$ ), in the Brillouin zone. We also study the nonequilibrium dynamics of a quantum generalization of a O(6) nonlinear $σ$ model of competing orders in the underdoped cuprates [Hayward et al., Science $\boldsymbol{343}$, 1336 (2014)]. We obtain results, in the large $N$ limit of a O($N$) model, on the time dependence of correlation functions following a pulse disturbance. We compare our numerical studies with recent picosecond optical experiments. We find that, generically, the oscillatory responses in our models share various qualitative features with the experiments.

cond-mat.supr-con↗

arXiv2014

Comment on "Symmetry classification of bond order parameters in cuprates"

We review the transformation of bond order waves with non-trivial form factors under time-reversal and point group symmetry. Zeyher (arXiv:1406.6846) argues that certain d-form factor states must be "flux states", but this does not apply to the form factors as defined by us (arXiv:1402.4807). The latter definitions were used in the experimental detection (arXiv:1402.5415, arXiv:1404.0362).

cond-mat.str-el↗

arXiv2014

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 wavevector $(π, π)$. This 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 the hot spots are perfectly nested or not, 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 $d_{x^2-y^2}$ superconducting and $d$-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wavevectors, and find dominant $d$-form factor enhancement for a range of couplings.

cond-mat.supr-con↗

arXiv2014

Diamagnetism and density wave order in the pseudogap regime of YBa$_2$Cu$_3$O$_{6+x}$

Clear experimental evidence of charge density wave correlations competing with superconducting order in YBCO have thrust their relationship with the pseudogap regime into the spotlight. To aid in characterizing the pseudogap regime, we propose a dimensionless ratio of the diamagnetic susceptibility to the correlation length of the charge density wave correlations. Using Monte Carlo simulations, we compute this ratio on the classical model of Hayward et. al. (Science 343, 1336 (2014)), which describes angular fluctuations of a multicomponent order, capturing both superconducting and density wave correlations. We compare our results with available data on YBa$_2$Cu$_3$O$_{6+x}$, and propose experiments to clarify the value of this dimensionless ratio using existing samples and techniques.

cond-mat.supr-con↗

arXiv2014

Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor

The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (Tc) superconducting mechanism. Here we employ magnetic-field-dependent scanning tunneling microscopy to provide phase-sensitive proof that d-wave superconductivity coexists with the pseudogap on the antinodal Fermi surface of an overdoped cuprate. Furthermore, by tracking the hole doping (p) dependence of the quasiparticle interference pattern within a single Bi-based cuprate family, we observe a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting Tc. Surprisingly, this major reorganization of the system's underlying electronic structure has no effect on the smoothly evolving pseudogap.

cond-mat.supr-con↗

arXiv2014

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates

The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO$_2$ unit-cell, segregating the results into three separate electronic structure images containing only the Cu sites (Cu(r)) and only the x/y-axis O sites (O$_x$(r) and O$_y$(r)). Phase resolved Fourier analysis reveals directly that the modulations in the O$_x$(r) and O$_y$(r) sublattice images consistently exhibit a relative phase of $π$. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intra-unit-cell states that exhibit a predominantly d-symmetry form factor.

cond-mat.supr-con↗

arXiv2014

Auxiliary-boson and DMFT studies of bond ordering instabilities of t-J-V models on the square lattice

We examine the influence of strong on-site Coulomb interactions on instabilities of the metallic state on the square lattice to general forms of bond order. The Mott correlations are accounted for by the auxiliary-boson method, and by dynamical mean field theory calculations, complementing our recent work (arXiv:1402.4807) using Gutzwiller projected variational wavefunctions. By the present methods, we find that the on-site Mott correlations do not significantly modify the structure of the bond ordering instabilities which preserve time-reversal symmetry, but they do enhance the instability towards time-reversal symmetry breaking "staggered flux" states.

cond-mat.str-el↗

arXiv2014

Transport near the Ising-nematic quantum critical point of metals in two dimensions

We consider two-dimensional metals near a Pomeranchuk instability which breaks 90$^\circ$ lattice rotation symmetry. Such metals realize strongly-coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation, and hence a non-zero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the $d$-wave channel acts as a random "field" on the Ising-nematic order. We find contributions to the resistivity with a nearly linear temperature dependence, along with more singular terms; the most singular is the random-field contribution which diverges in the limit of zero temperature.

cond-mat.str-el↗

arXiv2014

Bond order instabilities in a correlated two-dimensional metal

Motivated by recent experimental evidence of charge order in the pseudogap phase of cuprates, we perform a variational analysis of charge-neutral, spin-singlet ordering in metals on the square lattice, using a wavefunction with double occupancy projected out. We examine ordering with and without time-reversal symmetry, with arbitrary wavevector and tunable form factor. Depending on parameters, we find d-wave bond density wave ordering with wavevector either parallel to the lattice generators or diagonally oriented, or a ground state which carries a time reversal-breaking pattern of spontaneous currents.

cond-mat.str-el↗

arXiv2014

Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder

We compute the direct current resistivity of a scale-invariant, $d$-dimensional strange metal with dynamic critical exponent $z$ and hyperscaling-violating exponent $θ$, weakly perturbed by a scalar operator coupled to random-field disorder that locally breaks a $\mathbb{Z}_2$ symmetry. Independent calculations via Einstein-Maxwell-Dilaton holography and memory matrix methods lead to the same results. We show that random field disorder has a strong effect on resistivity: charge carriers in the infrared are easily depleted, as the relaxation time for momentum is surprisingly small. In the course of our holographic calculation we use a non-trivial dilaton coupling to the disordered scalar, allowing us to study a strongly-coupled scale invariant theory with $θ\ne 0$. Using holography, we are also able to determine the disorder strength at which perturbation theory breaks down. Curiously, for locally critical theories this breakdown occurs when the resistivity is proportional to the entropy density, up to a possible logarithmic correction.

hep-th↗

arXiv2014

Mean field theory of competing orders in metals with antiferromagnetic exchange interactions

It has long been known that two-dimensional metals with antiferromagnetic exchange interactions have a weak-coupling instability to the superconductivity of spin-singlet, d-wave electron pairs. We examine additional possible instabilities in the spin-singlet particle-hole channel, and study their interplay with superconductivity. We perform an unrestricted Hartree-Fock-BCS analysis of bond order parameters in a single band model on the square lattice with nearest-neighbor exchange and repulsion, while neglecting on-site interactions. The dominant particle-hole instability is found to be an incommensurate, bi-directional, bond density wave with wavevectors along the (1,1) and (1,-1) directions, and an internal d-wave symmetry. The magnitude of the ordering wavevector is close to the separation between points on the Fermi surface which intersect the antiferromagnetic Brillouin zone boundary. The temperature dependence of the superconducting and bond order parameters demonstrates their mutual competition. We also obtain the spatial dependence of the two orders in a vortex lattice induced by an applied magnetic field: "halos" of the bond order appear around the cores of the vortices.

cond-mat.supr-con↗

arXiv2014

Conformal field theories in a periodic potential: results from holography and field theory

We study 2+1 dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction $x$ with zero average: $μ(x) = V \cos(kx)$. The dynamics of such theories depends only on the dimensionless ratio $V/k$, and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of $V/k$. We compute the frequency-dependent conductivity of strongly-coupled CFTs using holography of the Einstein-Maxwell theory in 4-dimensional anti-de Sitter space. We compare the results with the corresponding computation of weakly-coupled CFTs, perturbed away from the CFT of free, massless Dirac fermions (which describes graphene at low energies). We find that the results of the two computations have significant qualitative similarities. However, differences do appear in the vicinities of an infinite discrete set of values of $V/k$: the universality class of the infrared CFT changes at these values in the weakly-coupled theory, by the emergence of new zero modes of Dirac fermions which are remnants of local Fermi surfaces. The infrared theory changes continuously in holography, and the classical gravitational theory does not capture the physics of the discrete transition points between the infrared CFTs. We briefly note implications for a non-zero average chemical potential.

hep-th↗

arXiv2013

Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors

The hole-doped cuprate high temperature superconductors enter the pseudogap regime as their superconducting critical temperature, $T_c$, falls with decreasing hole density. Experiments have probed this regime for over two decades, but we argue that decisive new information has emerged from recent X-ray scattering experiments (arXiv:1207.0915, arXiv:1206.4333, arXiv:1207.3667). The experiments observe incommensurate charge density wave fluctuations whose strength rises gradually over a wide temperature range above $T_c$, but then decreases as the temperature is lowered below $T_c$. We propose a theory in which the superconducting and charge-density wave orders exhibit angular fluctuations in a 6-dimensional space. The theory provides a natural quantitative fit to the X-ray data, and can be a basis for understanding other characteristics of the pseudogap.

cond-mat.supr-con↗

arXiv2013

The dynamics of quantum criticality via Quantum Monte Carlo and holography

Understanding the real time dynamics of quantum systems without quasiparticles constitutes an important yet challenging problem. We study the superfluid-insulator quantum-critical point of bosons on a two-dimensional lattice, a system whose excitations cannot be described in a quasiparticle basis. We present detailed quantum Monte Carlo results for two separate lattice realizations: their low-frequency conductivities are found to have the same universal dependence on imaginary frequency and temperature. We then use the structure of the real time dynamics of conformal field theories described by the holographic gauge/gravity duality to make progress on the difficult problem of analytically continuing the Monte Carlo data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point, and on the spectrum of quasinormal modes in the vicinity of the superfluid-insulator quantum phase transition. Extensions to other observables and universality classes are discussed.

cond-mat.str-el↗