arXiv subjects

Koenraad Schalm

Publications and source records attributed to Koenraad Schalm.

At least 19 recordsLinked to original sources

arXiv2025

Quantum critical theories in a periodic potential: strange metallic thermoelectric and magnetotransport

We study DC and AC thermoelectric and magneto-transport in 2D quantum critical theories with strong translational symmetry breaking due to a % varying chemical potential lattice with zero average $\bar{\mu}=0$. The combination of quantum criticality and the absence of the average natural scale implies that such systems have idiosyncratic signatures that may apply more generally when the variance in the lattice potential far exceeds the average or for strong translational symmetry breaking in general. We model such theories holographically through near-extremal AdS black holes. We find that these systems (a) become \emph{better} conductors. In a 2D lattice, this can be explained by currents flowing around obstacles; (b) exhibit bad-metal electrical transport with Drude-like thermal transport, though it is not Drude, and, notably, (c) display an approximately $B$-linear longitudinal magnetoresistance at large fields, similar to Effective Medium Theory. We comment on how these results may apply when $\bar{\mu}\neq 0$.

hep-th↗

arXiv2025

Josephson wormhole in coupled superconducting Yukawa-SYK metals

We show that two Yukawa-SYK models with a weak tunneling contact can have an exotic hybrid superconducting thermofield-double-like state that is holographically dual to a traversable wormhole connecting two black holes with charged scalar hair. The hybrid superconducting thermo-field-double/wormhole state is distinguishable by anomalous scaling of revival oscillations in the fermionic Green's function, but also in a unique Andreev-revival in the anomalous Green's function. The existence of this TFD/wormhole state surprisingly shows that the some quantum critical effects can survive the phase transition to superconductivity. This Andreev-revival is in principle an accessible signature of the transition to the TFD/wormhole phase detectable in the ac-Josephson current.

cond-mat.str-el↗

arXiv2024

Natural anomalous cyclotron response in a hydrodynamic local quantum critical metal in a periodic potential

We study DC magnetotransport in a quantum critical metal in the presence of a lattice. In the regime where the transport is hydrodynamical the interplay of the Lorentz force and the lattice gives rise to a natural anomalous contribution to the cyclotron frequency that changes it from its canonical charge-to-mass ratio. The size of this effect is universal as it is determined only by thermodynamic quantities. Remarkably the Drude weight changes in such a way that to first subleading order in the lattice strength the Hall resistivity and Hall coefficient do not change, though the Hall angle does change. We confirm our results with numerical simulations in a holographic model of a strange metal. For weak lattice strength these hydrodynamic effects are shown to be present. The numerical simulations also suggest that strong lattice effects beyond a hydrodynamic regime may provide a resolution to the experimentally observed anomalous Hall response of cuprate strange metals.

cond-mat.str-el↗

arXiv2024

Hydrodynamics of a relativistic charged fluid in the presence of a periodically modulated chemical potential

We study charged hydrodynamics in a periodic lattice background. Fluctuations are Bloch waves rather than single momentum Fourier modes. At boundaries of the unit cell where hydrodynamic fluctuations are formally degenerate with their Umklapped copy, level repulsion occurs. Novel mode mixings between charge, sound, and their Umklapped copies appear at finite chemical potential -- both at zero and finite momentum. We provide explicit examples for an ionic lattice, i.e. a periodic external chemical potential, and verify our results with numerical computations in fluid-gravity duality.

cond-mat.str-el↗

arXiv2023

T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential

High $T_c$ cuprate strange metals are noted for a DC-resistivity that scales linearly with $T$ from the onset of superconductivity to the crystal melting temperature, indicative of a Planckian dissipation life time $τ_{\hbar}\simeq \hbar /(k_B T)$. At the same time, the optical conductivity ceases to be of Drude form at high temperatures, suggesting a change of the underlying dynamics that surprisingly leaves the $T$-linear DC-resistivity unaffected. We use the AdS/CFT correspondence that describes strongly coupled, densely entangled metals to study DC thermo-electrical transport and the optical conductivities of the local quantum critical Gubser-Rocha holographic strange metal in the presence of a lattice potential, a prime candidate to compare with experiment. We find that the DC-resistivity is linear in $T$ at low temperatures for a range of lattice strengths and wavevectors, even as it transitions between different dissipative regimes. At weak lattice potential the optical conductivity evolves with increasing temperature from a Drude form to a bad-metal characterized by a mid-IR resonance without changing the DC transport, similar to that seen in cuprate strange metals. This mid-IR peak and its temperature evolution can be understood as a consequence of Umklapp hydrodynamics: hydrodynamic perturbations are Bloch modes in the presence of a lattice. At strong lattice potential an incoherent metal is realized instead where momentum conservation no longer plays a role in transport. In this regime the thermal diffusivity can be explained by Planckian dissipation originating in universal microscopic chaos, similar to holographic metals with strong homogeneous momentum relaxation. The charge diffusivity does not submit to this chaos explanation, even though the continuing linear-in-$T$ DC resistivity saturates to an apparent universal slope, numerically equal to a Planckian rate.

cond-mat.str-el↗

arXiv2023

Replicating Higgs fields in Ising gauge theory: the registry order

We consider $Z_2$ gauge field theory coupled to "Higgs" matter fields invoking several copies of such matter, interacting entirely through the gauge fields, the $Z_2 \times Z_2 \times Z_2\cdots / Z_2$ and the $O(N) \times O(N) \times O(N) \cdots / Z_2$ families of theories. We discover that the Higgs phase of such theories is characterized by a hitherto unidentified "registry" order parameter. This is characterized by a gauge invariant $p = 2^{N_{\text{rep}}}/2$ Potts type symmetry where $N_{\text{rep}}$ is the number of matter copies. The meaning of this registry is that the different matter copies align their vectors locally in strictly parallel or anti-parallel fashion, even dealing with the continuous $O(2)$ symmetry. Supported by Monte-Carlo simulations, we identify the origin of this registry order in terms of the gauge interactions mediated by the fluxes ("visons") associated with the $Z_2$ gauge fields, indirectly imposing the discrete symmetry in the gauge invariant global symmetry controlled effective order parameter theory. In addition, it appears that our simulations reveal a hitherto unidentified "pseudo-universality" associated with the very similar form of the overall phase diagrams of the various theories suggesting a remarkable "governance" by the gauge field part of the dynamics.

cond-mat.stat-mech↗

arXiv2023

Criticality versus uniformity in deep neural networks

Deep feedforward networks initialized along the edge of chaos exhibit exponentially superior training ability as quantified by maximum trainable depth. In this work, we explore the effect of saturation of the tanh activation function along the edge of chaos. In particular, we determine the line of uniformity in phase space along which the post-activation distribution has maximum entropy. This line intersects the edge of chaos, and indicates the regime beyond which saturation of the activation function begins to impede training efficiency. Our results suggest that initialization along the edge of chaos is a necessary but not sufficient condition for optimal trainability.

cs.LG↗

arXiv2023

Quantization and variational problem of the Gubser-Rocha Einstein-Maxwell-Dilaton model, conformal and non-conformal deformations, and its proper thermodynamics

We show that the strongly coupled field theory holographically dual to the Gubser-Rocha anti-de-Sitter Einstein-Maxwell-Dilaton theory describes not a single non-trivial AdS$_2$ IR fixed point, but a one-parameter family. It is dual to a local quantum critical phase instead of a quantum critical point. This result follows from a detailed analysis of the possible quantizations of the gravitational theory that is consistent with the thermodynamics of the analytical Gubser-Rocha black hole solution. The analytic Gubser-Rocha black hole is only a 2-parameter subset of all possible solutions, and we construct other members numerically. These new numerical solutions correspond to turning on an additional scalar charge. Moreover, each solution has multiple holographic interpretations depending on the quantization chosen. In one particular quantization involving a multitrace deformation the scalar charge is a marginal operator. In other quantizations where the marginal multitrace operator is turned off, the analytic Gubser-Rocha black hole does not describe a finite temperature conformal fluid.

hep-th↗

arXiv2022

Emerging Fermi liquids from regulated Quantum Electron Stars

We construct a fully quantum zero-temperature electron star in a soft-wall regulated anti-de-Sitter Einstein-Maxwell-Dirac theory that is thermodynamically stable compared to the Reissner-Nordström black hole. The soft wall only acts on the effective mass of the fermionic degrees of freedom, and allows for a controlled fully backreacted solution. The star is holographically dual to an RG flow where a gapped Fermi liquid starts to emerge from a UV CFT, but decouples again once the effective energy scale becomes lower than the the gap of the fermionic degrees of freedom. The RG flow then returns to a non-trivial strongly coupled relativistic fixed point with a holographic dual. Our regulated quantum electron star is thus the fermionic analogue of the Horowitz-Roberts-Gubser-Rocha AdS-to-AdS domain wall solution for the holographic superconductor.

hep-th↗

arXiv2021

Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals

Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the BCS theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction of ill-defined fermions, the latter is rooted in the duality of quantum field theory and gravity theory. We demonstrate that both are different perspectives of the same theory. We derive holographic superconductivity in form of a gravity theory with emergent space-time from a quantum many-body Hamiltonian - the Yukawa SYK model - where the Eliashberg formalism is exact. Exploiting the power of holography, we then determine the dynamic pairing susceptibility of the model. Our holographic map comes with the potential to use quantum gravity corrections to go beyond the Eliashberg regime.

cond-mat.str-el↗

arXiv2019

Operator thermalization vs eigenstate thermalization

We study the characteristics of thermalizing and non-thermalizing operators in integrable theories as we turn on a non-integrable deformation. Specifically, we show that $σ^z$, an operator that thermalizes in the integrable transverse field Ising model, has mean matrix elements that resemble ETH, but with fluctuations around the mean that are sharply suppressed. This suppression rapidly dwindles as the Ising model becomes non-integrable by the turning on of a longitudinal field. We also construct a non-thermalizing operator in the integrable regime, which slowly approaches the ETH form as the theory becomes non-integrable. At intermediate values of the non-integrable deformation, one distinguishes a perturbatively long relaxation time for this operator.

cond-mat.stat-mech↗

arXiv2019

Isolated zeros destroy Fermi surface in holographic models with a lattice

We study the fermionic spectral density in a strongly correlated quantum system described by a gravity dual. In the presence of periodically modulated chemical potential, which models the effect of the ionic lattice, we explore the shapes of the corresponding Fermi surfaces, defined by the location of peaks in the spectral density at the Fermi level. We find that at strong lattice potentials sectors of the Fermi surface are unexpectedly destroyed and the Fermi surface becomes an arc-like disconnected manifold. We explain this phenomenon in terms of a collision of the Fermi surface pole with zeros of the fermionic Green's function, which are explicitly computable in the holographic dual.

hep-th↗

arXiv2019

Thermalization/Relaxation in integrable and free field theories: an Operator Thermalization Hypothesis

Free or integrable theories are usually considered to be too constrained to thermalize. For example, the retarded two-point function of a free field, even in a thermal state, does not decay to zero at long times. On the other hand, the magnetic susceptibility of the critical transverse field Ising is known to thermalize, even though that theory can be mapped by a Jordan-Wigner transformation to that of free fermions. We reconcile these two statements by clarifying under which conditions conserved charges can prevent relaxation at the level of linear response and how such obstruction can be overcome. In particular, we give a necessary condition for the decay of retarded Green's functions. We give explicit examples of composite operators in free theories that nevertheless satisfy that condition and therefore do thermalize. We call this phenomenon the Operator Thermalization Hypothesis as a converse to the Eigenstate Thermalization Hypothesis.

cond-mat.stat-mech↗

arXiv2019

Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?

We study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value, including its Lyapunov spectrum, depends sensitively on the shape of the complex time contour in generic weakly coupled field theories. For gapless theories with no thermal mass, such as SYK, the Lyapunov spectrum turns out to be an exception; their Lyapunov spectra do not exhibit contour dependence, though the full OTOCs do. Our result puts into question which of the Lyapunov exponents computed from the exponential growth of the OTOC reflects the actual physical dynamics of the system. We argue that, in a weakly coupled $Φ^4$ theory, a kinetic theory argument indicates that the symmetric configuration of the time contour, namely the one for which the bound on chaos has been proven, has a proper interpretation in terms of dynamical chaos. Finally, we point out that a relation between these OTOCs and a quantity which may be measured experimentally --- the Loschmidt echo --- also suggests a symmetric contour configuration, with the subtlety that the inverse periodicity in Euclidean time is half the physical temperature. In this interpretation the chaos bound reads $λ\leq \frac{2π}β= πT_{\text{physical}}$.

hep-th↗

arXiv2019

Anomalous attenuation of plasmons in strange metals and holography

The plasmon is a ubiquitous collective mode in charged liquids. Due to the long-range Coulomb interaction, the massless zero sound mode of the neutral system acquires a finite plasmon frequency in the long-wavelength limit. In the zero-temperature state of conventional metals -- the Fermi liquid -- the plasmon lives infinitely long at long wavelength when the system is (effectively) translationally invariant. In contrast, we will show that in strongly entangled strange metals the protection of zero sound fails at finite frequency and plasmons are always short lived regardless of their wavelength. Computing the explicit plasmon response in holographic strange metals as an example, we show that decay into the quantum critical continuum replaces Landau damping and this happens for any wavelength.

cond-mat.str-el↗

arXiv2019

Isolated zeros in the spectral function as signature of a quantum continuum

We study the observable properties of quantum systems which involve a quantum continuum as a subpart. We show in a very general way that in any system, which consists of at least two isolated states coupled to a continuum, the spectral function of one of the states exhibits an isolated zero at the energy of the other state. Several examples of quantum systems exhibiting such isolated zeros are discussed. Although very general, this phenomenon can be particularly useful as an indirect detection tool for the continuum spectrum in the lab realizations of quantum critical behavior.

cond-mat.str-el↗

arXiv2019

Kinetic theory for classical and quantum many-body chaos

For perturbative scalar field theories, the late-time-limit of the out-of-time-ordered correlation function that measures (quantum) chaos is shown to be equal to a Boltzmann-type kinetic equation that measures the total gross (instead of net) particle exchange between phase space cells, weighted by a function of energy. This derivation gives a concrete form to numerous attempts to derive chaotic many-body dynamics from ad hoc kinetic equations. A period of exponential growth in the total gross exchange determines the Lyapunov exponent of the chaotic system. Physically, the exponential growth is a front propagating into an unstable state in phase space. As in conventional Boltzmann transport, which follows from the dynamics of the net particle number density exchange, the kernel of this kinetic integral equation is also set by the 2-to-2 scattering rate. This provides a mathematically precise statement of the known fact that in dilute weakly coupled gases transport and scrambling (or ergodicity) are controlled by the same physics.

hep-th↗

arXiv2018

A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled

In the AdS/CFT correspondence eternal black holes can be viewed as a specific entanglement between two copies of the CFT: the thermofield double. The statistical CFT Wightman function can be computed from a geodesic between the two boundaries of the Kruskal extended black hole and therefore probes the geometry behind the horizon. We construct a kernel for the AdS3/CFT2 Wightman function that is independent of the entanglement. This kernel equals the average off-diagonal matrix element squared of a primary operator. This allows us to compute the Wightman function for an arbitrary entanglement between the double copies and probe the emergent geometry between a left- and right-CFT that are not thermally entangled.

hep-th↗