arXiv subjects

Nicolas Chagnet

Publications and source records attributed to Nicolas Chagnet.

7 recordsLinked to original sources

arXiv2025

CFT Complexity and Penalty Factors

Quantum complexity of conformal field theory (CFT) states has recently gained significant attention, both as a diagnostic tool in condensed matter systems and in connection with holographic observables probing black hole interiors. Previous studies have primarily focused on cases where all generators of the conformal group contribute equally to the cost of building a circuit. In this work, we present a general framework for studying the complexity of circuits in generic Lie groups, where penalty factors assign relative weights to different generators. Our approach constructs a metric on the coset space of quantum states, induced from a (pseudo-)Riemannian norm on the space of unitary circuits. The geodesics of this metric are interpreted as optimal circuits. The method builds on the formalism of (pseudo-)Riemannian submersions and connects naturally to other prescriptions in the literature, including cost function minimization along stabilizer directions and constructions based on coadjoint orbits. As a concrete application, we compute state complexity for states in one- and two-dimensional CFTs. For specific choices of penalty factors, our prescription yields a positive-definite metric with a viable interpretation as complexity; in other cases, the resulting metric is indefinite. In the viable regime, we derive analytic results when a specific penalty factor is turned off, develop perturbative expansions for small values of the penalty factors, and provide numerical results in the general case. We comment on the relation of our measure of complexity to holography.

hep-th↗

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↗

arXiv2023

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↗

arXiv2022

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 $\tau_{\hbar}\simeq \hbar /(k_B T)$. 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↗

arXiv2022

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

Complexity for Conformal Field Theories in General Dimensions

We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance functions can be understood in terms of the geometry of coadjoint orbits of the conformal group. We explicitly relate our circuits to timelike geodesics in anti-de Sitter space and the complexity metric to distances between these geodesics. We extend our method to circuits in other symmetry groups using a group theoretic generalization of the notion of coherent states.

hep-th↗