arXiv subjects

Per Moosavi

Publications and source records attributed to Per Moosavi.

At least 19 recordsLinked to original sources

arXiv2026

Fluctuation-dissipation structure of quantum geometry

The geometry of quantum states is a fundamental research area with applications ranging from band theory in condensed matter to variational algorithms in quantum information. Due to their relative simplicity, pure states are usually studied, while mixed ones are needed in general, for instance to allow for finite temperatures. The geometry of mixed states, however, is much more challenging, with important aspects yet to be explored. Here, we provide one missing piece by identifying the structure that relates distance measure and curvature for general (mixed or pure) quantum states. This structure is shown to carry the physical meaning of fluctuation-dissipation---by directly relating distance measure with fluctuations and curvature with linear response---and it turns into the corresponding well-known structure for pure states, where it is K\"ahler, and only then. We thus obtain a general, simple fluctuation-dissipation picture, which, among its consequences, implies that response functions inherently probe the mixed-state quantum geometric tensor. We end by using this picture to give geometric characterizations of generic transport behaviors.

quant-ph↗

arXiv2025

Nonequilibrium Probes of Quantum Geometry in Gapless Systems

Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by their conformal symmetry. We reveal the underlying quantum geometry by considering finite many-body systems driven by time-dependent conformal transformations. For small deformations, perturbation theory predicts absorption rates and linear responses that probe the quantum geometric tensor. For arbitrarily large but adiabatic deformations, we show that periodic drives give rise to nontrivial return amplitudes involving the quantum metric, beyond the familiar leading order that only features a Berry phase. The former is less sensitive to decoherence than the latter, so it can provide robust experimental signatures of our predictions. Our field-theoretic findings are universal, comprising general relations between measurable quantities and quantum geometry that only depend on the emergent effective description. This is supported both by numerical simulations of gapless lattice models, and by exact results for quantum dynamics under certain Floquet drives, probing the full dynamical parameter space.

cond-mat.str-el↗

arXiv2025

Chiral Instabilities in Driven-Dissipative Quantum Liquids

We investigate the nonequilibrium dynamics of periodically driven Tomonaga-Luttinger liquids (TLLs) coupled to a thermal bath using a Floquet-Lindblad approach. When the coupling to the bath satisfies detailed balance, we obtain a condition for parametric instabilities to be suppressed, symmetrically for both chiralities. Remarkably, by designing a purely chiral coupling to the bath, instead of instability suppression, we uncover a driven-dissipative phase transition between the former symmetric parametric instability and a new chiral parametric instability. In the latter, a single chirality of bosonic quasiparticles gets exponentially amplified, leading to a dynamical chiral imbalance within the TLL, reminiscent of the non-Hermitian skin effect.

cond-mat.stat-mech↗

arXiv2024

Perfect Wave Transfer in Continuous Quantum Systems

The transfer of information from one part of a quantum system to another is fundamental to the understanding and design of quantum information processing devices. In the realm of discrete systems such as spin chains, inhomogeneous networks have been engineered that allow for the perfect transfer of qubits from one end to the other. Here, by contrast, we investigate the perfect transfer of information in continuous systems, phrased in terms of wave propagation. A remarkable difference is found between systems that possess conformal invariance and those that do not. Systems in the first class enjoy perfect wave transfer (PWT), explicitly shown for one-particle excitations and anticipated in general. In the second class, those that exhibit PWT are characterized as solutions to an inverse spectral problem. As a concrete example, we demonstrate how to formulate and solve this problem for a prototypical class of bosonic theories, showing the importance of conformal invariance for these theories to enjoy PWT. Using bosonization, our continuum results extend to theories with interactions, broadening the scope of perfect information transfer to more general quantum systems.

quant-ph↗

arXiv2024

Quantum Hall edges beyond the plasma analogy

We demonstrate that the widely used plasma analogy is unreliable at predicting edge properties of quantum Hall states. This discrepancy arises from a fundamental difference between quantum Hall droplets and plasmas (Coulomb gases): the former are incompressible liquids subject to area-preserving deformations, while the latter are governed by electrostatics and thus involve conformal transformations. Consequently, the plasma analogy fails at the edge, except in fine-tuned geometries, as it does not account for the emergent local edge velocity. We quantitatively show how the analogy's failure affects physical quantities, such as fluctuations of local observables and absorption rates in microwave spectroscopy, measurable in both solid-state experiments and quantum simulators.

cond-mat.mes-hall↗

arXiv2023

Anisotropic Quantum Hall Droplets

We study two-dimensional (2D) droplets of noninteracting electrons in a strong magnetic field, placed in a confining potential with arbitrary shape. Using semiclassical methods adapted to the lowest Landau level, we obtain near-Gaussian energy eigenstates that are localized on level curves of the potential and have a position-dependent height. This one-particle insight allows us to deduce explicit formulas for expectation values of local many-body observables, such as density and current, in the thermodynamic limit. In particular, correlations along the edge are long-ranged and inhomogeneous. As we show, this is consistent with the system's universal low-energy description as a free 1D chiral conformal field theory of edge modes, known from earlier works in simple geometries. A delicate interplay between radial and angular dependencies of eigenfunctions ultimately ensures that the theory is homogeneous in terms of the canonical angle variable of the potential, despite its apparent inhomogeneity in terms of more na\"ive angular coordinates. Finally, we propose a scheme to measure the anisotropy by subjecting the droplet to microwave radiation; we compute the corresponding absorption rate and show that it depends on the droplet's shape and the waves' polarization. These results, both local and global, are likely to be observable in solid-state systems or quantum simulators of 2D electron gases with a high degree of control on the confining potential.

cond-mat.mes-hall↗

arXiv2022

Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids

We study inhomogeneous 1+1-dimensional quantum many-body systems described by Tomonaga-Luttinger-liquid theory with general propagation velocity and Luttinger parameter varying smoothly in space, equivalent to an inhomogeneous compactification radius for free boson conformal field theory. This model appears prominently in low-energy descriptions, including for trapped ultracold atoms, while here we present an application to quantum Hall edges with inhomogeneous interactions. The dynamics is shown to be governed by a pair of coupled continuity equations identical to inhomogeneous Dirac-Bogoliubov-de Gennes equations with a local gap and solved by analytical means. We obtain their exact Green's functions and scattering matrix using a Magnus expansion, which generalize previous results for conformal interfaces and quantum wires coupled to leads. Our results explicitly describe the late-time evolution following quantum quenches, including inhomogeneous interaction quenches, and Andreev reflections between coupled quantum Hall edges, revealing a remarkably universal dependence on details at stationarity or at late times out of equilibrium.

cond-mat.stat-mech↗

arXiv2022

Marginal quenches and drives in Tomonaga-Luttinger liquids

We study Tomonaga-Luttinger liquids thrown out of equilibrium by marginal deformations in the form of interaction modulations. This is modeled by quenching or periodically driving the Luttinger parameter or, equivalently, the compactification radius of the free boson conformal field theory between two different values. We obtain exact analytical results for the evolution of the Loschmidt echo and observables such as the particle and energy densities. Starting from generic initial states, the quench dynamics are shown to exhibit revivals and temporal orthogonalities. For the periodic drive, we show stability or instability of time-evolved physical quantities dependent on the drive parameters. We also compare the corresponding marginally deformed thermal density matrices by non-perturbatively evaluating their R\'{e}nyi divergence as a Euclidean quench. All the dynamics are shown to be crucially dependent on the ratio of the Luttinger parameters, which corresponds to the Zamolodchikov distance in the space of marginal deformations. Our setup is equivalently interpreted as the dynamics of the bosonic string upon instantaneous changes of the target-space radius.

cond-mat.stat-mech↗

arXiv2021

Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids

Tomonaga-Luttinger liquids (TLLs) can be used to effectively describe one-dimensional quantum many-body systems such as ultracold atoms, charges in nanowires, superconducting circuits, and gapless spin chains. Their properties are given by two parameters, the propagation velocity and the Luttinger parameter. Here we study inhomogeneous TLLs where these are promoted to functions of position and demonstrate that they profoundly affect the dynamics: In general, besides curving the light cone, we show that propagation is no longer ballistically localized to the light-cone trajectories, different from standard homogeneous TLLs. Specifically, if the Luttinger parameter depends on position, the dynamics features pronounced spreading into the light cone, which cannot be understood via a simple superposition of waves as in the Huygens-Fresnel principle. This is the case for ultracold atoms in a parabolic trap, which serves as our main motivation, and we discuss possible experimental observations in such systems.

cond-mat.stat-mech↗

arXiv2020

Stability of the classical catenoid and Darboux-P\"oschl-Teller potentials

We revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable one-dimensional Schr\"odinger operator with an asymmetric Darboux-P\"oschl-Teller potential.

math-ph↗

arXiv2020

Geometric approach to inhomogeneous Floquet systems

We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the $\mathfrak{sl}(2)$ algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory.

cond-mat.stat-mech↗

arXiv2020

Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons

We construct and study relativistic anyons in 1+1 dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) by adding density-density interactions, as in the Luttinger model, and (ii) by coupling the free anyons to a U(1)-gauge field, as in the Schwinger model. Second, physical properties of these extensions are studied. By investigating off-diagonal long-range order (ODLRO) at zero temperature, we show that anyonic statistics allows one to get arbitrarily close to ODLRO but that this possibility is destroyed by the gauge coupling. The latter is due to a nonzero effective mass generated by gauge invariance, which we show also implies the presence of screening, independently of the anyonic statistics.

cond-mat.stat-mech↗

arXiv2020

Emergence of generalized hydrodynamics in the non-local Luttinger model

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

cond-mat.stat-mech↗

arXiv2019

Inhomogeneous conformal field theory out of equilibrium

We study the non-equilibrium dynamics of conformal field theory (CFT) in 1+1 dimensions with a smooth position-dependent velocity $v(x)$ explicitly breaking translation invariance. Such inhomogeneous CFT is argued to effectively describe 1+1-dimensional quantum many-body systems with certain inhomogeneities varying on mesoscopic scales. Both heat and charge transport are studied, where, for concreteness, we suppose that our CFT has a conserved U$(1)$ current. Based on projective unitary representations of diffeomorphisms and smooth maps in Minkowskian CFT, we obtain a recipe for computing the exact non-equilibrium dynamics in inhomogeneous CFT when evolving from initial states defined by smooth inverse-temperature and chemical-potential profiles $\beta(x)$ and $\mu(x)$. Using this recipe, the following exact analytical results are obtained: (i) the full time evolution of densities and currents for heat and charge transport, (ii) correlation functions for components of the energy-momentum tensor and the U$(1)$ current as well as for any primary field, and (iii) the thermal and electrical conductivities. The latter are computed by direct dynamical considerations and alternatively using a Green-Kubo formula. Both give the same explicit expressions for the conductivities, which reveal how inhomogeneous dynamics opens up the possibility for diffusion as well as implies a generalization of the Wiedemann-Franz law to finite times within CFT.

math-ph↗

arXiv2018

Diffusive Heat Waves in Random Conformal Field Theory

We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a nontrivial real regular contribution that depends on details of the impurities.

cond-mat.stat-mech↗

arXiv2017

Finite-time universality in nonequilibrium CFT

Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.

cond-mat.stat-mech↗

arXiv2017

Time evolution of the Luttinger model with nonuniform temperature profile

We study the time evolution of a one-dimensional interacting fermion system described by the Luttinger model starting from a nonequilibrium state defined by a smooth temperature profile $T(x)$. As a specific example we consider the case when $T(x)$ is equal to $T_L$ ($T_R$) far to the left (right). Using a series expansion in $\epsilon = 2(T_{R} - T_{L})/(T_{L}+T_{R})$, we compute the energy density, the heat current density, and the fermion two-point correlation function for all times $t \geq 0$. For local (delta-function) interactions, the first two are computed to all orders, giving simple exact expressions involving the Schwarzian derivative of the integral of $T(x)$. For nonlocal interactions, breaking scale invariance, we compute the nonequilibrium steady state (NESS) to all orders and the evolution to first order in $\epsilon$. The heat current in the NESS is universal even when conformal invariance is broken by the interactions, and its dependence on $T_{L,R}$ agrees with numerical results for the $XXZ$ spin chain. Moreover, our analytical formulas predict peaks at short times in the transition region between different temperatures and show dispersion effects that, even if nonuniversal, are qualitatively similar to ones observed in numerical simulations for related models, such as spin chains and interacting lattice fermions.

cond-mat.stat-mech↗

arXiv2015

Steady states and universal conductance in a quenched Luttinger model

We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian $H_{\lambda}$ with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time $t>0$ via a Hamiltonian $H_{\lambda'}$ which differs from $H_{\lambda}$ by the strength of the interaction. Asymptotically in time, as $t \to \infty$, after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current $I$ and has an effective chemical potential difference $\mu_+ - \mu_-$ between right- ($+$) and left- ($-$) moving fermions obtained from the two-point correlation function. Both $I$ and $\mu_+ - \mu_-$ depend on $\lambda$ and $\lambda'$. Only for the case $\lambda = \lambda' = 0$ does $\mu_+ - \mu_-$ equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, $G=I/(\mu_+ - \mu_-)$, has a universal value equal to the conductance quantum $e^2/h$ for the spinless case.

math-ph↗