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Subir Sachdev

Publications and source records attributed to Subir Sachdev.

At least 73 records · Page 4Linked to original sources
arXiv2024

Localization of overdamped bosonic modes and transport in strange metals

A recent theory described strange metal behavior in a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for wide range of intermediate temperatures, including the linear-in-temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an $M$-component boson with $M \geq 2$, we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a `quantum critical phase' away from the quantum critical point, as observed in several cuprates. For the $M = 1$ Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.

cond-mat.str-el↗
arXiv2024

Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations

Disorder at the etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially-filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edge states in the graphene electrodes to measure electrical conductance and thermoelectric power across the GQD. We observe a rapid diminishing of electric conductance fluctuations and slowly decreasing thermoelectric power across the GQD with increasing temperature, consistent with recent theoretical predictions for the SYK regime.

cond-mat.mes-hall↗
arXiv2024

Strange metals and black holes: insights from the Sachdev-Ye-Kitaev model

Complex many-particle quantum entanglement is a central theme in two distinct major topics in physics: the strange metal state found in numerous correlated electron compounds, and the quantum theory of black holes in Einstein gravity. The Sachdev-Ye-Kitaev model provides a solvable theory of entangled many-particle quantum states without quasiparticle excitations. This article reviews how this toy model has led to realistic universal models of strange metals, and to new insights on the quantum states of black holes.

cond-mat.str-el↗
arXiv2024

Cyclotron resonance and quantum oscillations of critical Fermi surfaces

Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of La$_{2-x}$Sr$_x$CuO$_4$ (Legros et al., Phys. Rev. B 106, 195110 (2022)) are therefore surprising because the cyclotron mass can only be renormalized by large momentum umklapp interactions which are not expected to vary significantly with doping. We show that a version of Kohn's theorem continues to apply to disorder-free non-Fermi liquids with a critical boson near zero momentum. However, marginal Fermi liquids arising from a spatially random Yukawa coupling between the electrons and bosons do give rise to significant corrections to the cyclotron mass which we compute. This is the same theory which yields linear-in-temperature resistivity and other properties of strange metals at zero fields (Patel et al., Science 381, 790 (2023)).

cond-mat.str-el↗
arXiv2024

Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula

Relating the quantized Hall response of correlated insulators to many-body topological invariants is a key challenge in topological quantum matter. Here, we use Streda's formula to derive an expression for the many-body Chern number in terms of the single-particle interacting Green's function and its derivative with respect to a magnetic field. In this approach, we find that this many-body topological invariant can be decomposed in terms of two contributions, $N_3[G] + ΔN_3[G]$, where $N_3[G]$ is known as the Ishikawa-Matsuyama invariant and where the second term involves derivatives of Green's function and the self energy with respect to the magnetic perturbation. As a by-product, the invariant $N_3[G]$ is shown to stem from the derivative of Luttinger's theorem with respect to the probe magnetic field. These results reveal under which conditions the quantized Hall conductivity of correlated topological insulators is solely dictated by the invariant $N_3[G]$, providing new insight on the origin of fractionalization in strongly-correlated topological phases.

cond-mat.str-el↗
arXiv2023

Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons

The pseudogap metal phase of the hole-doped cuprates can be described by small Fermi surfaces of electron-like quasiparticles, which enclose a volume violating the Luttinger relation. This violation requires the existence of additional fractionalized excitations which can be viewed as fractionalized remnants of the paramagnon. We fractionalize the paramagnon into bosonic spinons, and present a gauge theory of bosonic spinons, a Higgs field, and an ancilla layer of fermions coupled to the original electrons. Along with the small Fermi surface metal, this theory displays conventional phases: the Fermi liquid with a low-energy paramagnon mode, and phases with spin density wave order. We follow the evolution of the electronic photoemission spectrum across these quantum phase transitions. We consider both the two-sublattice Néel and incommensurate spin density wave phases.

cond-mat.str-el↗
arXiv2023

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. For instance, recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of unusual consequences: most notably, the pairing invariant under all symmetries can have protected nodal lines or be fully gapped, depending on parameters, and the band-off-diagonal chiral d-wave state exhibits transitions between gapped and nodal regions upon varying the chemical potential. We demonstrate that nodal band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley-coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

cond-mat.supr-con↗
arXiv2023

Sign-problem-free effective models of triangular lattice quantum antiferromagnets

The triangular lattice antiferromagnet with $S=1/2$ spins and nearest neighbor interactions is known to have long-range antiferromagnetic order, with nearest-neighbor spins at an angle of 120 degrees. Numerical studies of quantum phases proximate to this state have been limited to small systems because the of the sign-problem in Monte Carlo simulations in imaginary time. We propose an effective lattice model for quantum fluctuations of the antiferromagnetic order, and a sign-problem free Monte Carlo algorithm, enabling studies in large systems sizes. The model is a $\mathbb{Z}_2$ gauge theory coupled to gauge-charged scalars which have a relativistic dispersion in the continuum limit. Crucially, the gauge theory is odd, i.e. there is a static, background $\mathbb{Z}_2$ gauge charge on each site, accounting for the Berry phases of the half-odd-integer spins on each site. We present results of simulations on lattices of sizes up to $36 \times 36 \times 36$. Along with the antiferromagnetically ordered phase, our phase diagram has a valence bond solid state with a $\sqrt{12} \times \sqrt{12}$ unit cell, and a gapped $\mathbb{Z}_2$ spin liquid. Deconfined critical points or phases in intermediate regions are not ruled out by our present simulations.

cond-mat.str-el↗
arXiv2023

Disordered quantum critical fixed points from holography

Using holographic duality, we present an analytically controlled theory of quantum critical points without quasiparticles, at finite disorder and finite charge density. These fixed points are obtained by perturbing a disorder-free quantum critical point with relevant disorder whose operator dimension is perturbatively close to Harris marginal. We analyze these fixed points both using field theoretic arguments, and by solving the bulk equations of motion in holography. We calculate the critical exponents of the IR theory, together with thermoelectric transport coefficients. Our predictions for the critical exponents of the disordered fixed point are consistent with previous work, both in holographic and nonholograpic models.

cond-mat.str-el↗
arXiv2023

Conductance and thermopower fluctuations in interacting quantum dots

We model an interacting quantum dot of electrons by a Hamiltonian with random and all-to-all single particle hopping (of r.m.s. strength $t$) and two-particle interactions (of r.m.s. strength $J$). For $t \ll J$, such a model has a regime exhibiting the non-quasiparticle physics of the Sachdev-Ye-Kitaev model at temperatures $E_{\rm coh} \ll T \ll J$, and that of a renormalized Fermi liquid at $T \ll E_{\rm coh}$, where $E_{\rm coh} = t^2 / J$. Extending earlier work has computed the mean thermoelectric properties of such a dot weakly coupled to two external leads, we compute the sample-to-sample fluctuations in the conductance and thermopower of such a dot, and describe several distinct regimes. In all cases, the effect of the SYK interactions is to reduce the strength of the sample-to-sample fluctuations. We also find that in the regime where the mean transport co-efficients are determined only by the value of $J$ at leading order, the sample-to-sample fluctuations can be controlled by the influence of the smaller $t$.

cond-mat.str-el↗
arXiv2023

Theory of shot noise in strange metals

We extend the theory of shot noise in coherent metals to shot noise in strange metals without quasiparticle excitations. This requires a generalization of the Boltzmann equation with a noise source to distribution functions which depend independently on the excitation momentum and energy. We apply this theory to a model of a strange metal with linear in temperature ($T$) resistivity, describing a Fermi surface with a spatially random Yukawa coupling to a critical boson. We find a suppression of the Fano factor in the strange metal, and describe the dependence of the shot noise on temperature and applied voltage. At low temperatures, we obtain a Fano factor equal to $1/6$, in contrast to the $1/3$ Fano factor in diffusive metals with quasiparticles. Our results are in general agreement with recent observations by Chen et al. (arXiv:2206.00673). We further compare the random Yukawa model to quasi-elastic electron-phonon scattering that also generates $T$-linear resistivity, and argue that shot noise observations offer a useful diagnostic to distinguish between them.

cond-mat.str-el↗
arXiv2023

Equilibrium dynamics of infinite-range quantum spin glasses in a field

We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ($h$) fields. We show that, for all $h$, the spin glass state has full replica symmetry breaking, and the local spin spectrum is gapless with a spectral density which vanishes linearly with frequency. These results are obtained using an action functional$\unicode{x2014}$argued to yield exact results at low frequencies$\unicode{x2014}$that expands in powers of a spin glass order parameter, which is is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum $p$-rotor model at nonzero $h$: here, the spin glass state has one-step replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted.

cond-mat.dis-nn↗
arXiv2023

Large $N$ theory of critical Fermi surfaces II: conductivity

A Fermi surface coupled to a scalar field can be described in a $1/N$ expansion by choosing the fermion-scalar Yukawa coupling to be random in the $N$-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and verify that the proposed $1/ω^{2/3}$ contribution to the optical conductivity at frequency $ω$ has vanishing co-efficient for a convex Fermi surface. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity and optical conductivity behave like a Fermi liquid.

cond-mat.str-el↗
arXiv2023

Universal theory of strange metals from spatially random interactions

We consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or emergent gauge fields. We show that at low temperatures ($T$), such metals generically exhibit strange metal behavior with a $T$-linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a non-zero spatial average. We also find a $T\ln (1/T)$ specific heat, and a rationale for the Planckian bound on the transport scattering time. These results are obtained in the large $N$ expansion of an ensemble of critical metals.

cond-mat.str-el↗
arXiv2023

Emergent glassy behavior in a kagome Rydberg atom array

We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal \textit{emergent} glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids -- as well as the crossover towards a trivial paramagnetic phase -- are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.

cond-mat.quant-gas↗
arXiv2023

Classifying topological neural network quantum states via diffusion maps

We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave functions with probability decaying exponentially with their variational energy; this defines our training dataset that we use as input to a diffusion map scheme. The diffusion map provides a low-dimensional embedding of the wave functions, revealing the presence or absence of superselection sectors and, thus, topological order. We show that for the diffusion map, the required similarity measure of quantum states can be defined in terms of the network parameters, allowing for an efficient evaluation within polynomial time. However, possible ''gauge redundancies'' have to be carefully taken into account. As an explicit example, we apply the method to the toric code.

quant-ph↗
arXiv2022

Statistical mechanics of strange metals and black holes

A colloquium style review of the connections between the Sachdev-Ye-Kitaev model and strange metals without quasiparticles, and between the SYK model and the quantum properties of black holes. Along with other insights, this connection has led to an understanding of the universal form of the low energy density of states of charged black holes in asymptotically 3+1 dimensional Minkowski space.

hep-th↗
arXiv2022

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the $t$-$J$ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large $N$ theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions.

cond-mat.str-el↗