arXiv subjects

Gábor Takács

Publications and source records attributed to Gábor Takács.

At least 19 recordsLinked to original sources

arXiv2026

Full counting statistics in the sine-Gordon model

Full counting statistics (FCS) is a dynamical generalisation of the free energy, encapsulating detailed information about the distribution and large-scale correlation functions of conserved charges and their associated currents. In this work, we present a comprehensive numerical study of the FCS and the cumulants of the three lowest charges across the full parameter space of the sine-Gordon field theory. To this end, we extend the thermodynamic Bethe Ansatz (TBA) formulation of the FCS to the sine-Gordon model, emphasise the methodological subtleties for a reliable numerical implementation, and compare numerical results with analytical predictions in certain limits.

cond-mat.stat-mech↗

arXiv2026

Confinement in the three-state Potts quantum spin chain in extreme ferromagnetic limit

We investigate the dynamics of the three-state Potts quantum spin chain in the extreme ferromagnetic limit using a perturbative expansion in the transverse magnetic field. We demonstrate that a perturbative approach provides access to important features beyond the reach of previous studies, most notably the description of resonant excitations and the analytic prediction of post-quench time evolution. A central focus is the oblique quench regime - a feature unique to the Potts model with no Ising counterpart - in which unconfined kink excitations hybridise with the two-kink bound states. We provide a detailed examination of the analytic structure of the two-kink scattering amplitude, tracing the transformation of stable excitations into resonances near stability thresholds. Our analytical results for the excitation spectra and magnetisation dynamics show excellent agreement with numerical simulations of non-equilibrium dynamics.

cond-mat.stat-mech↗

arXiv2025

Confinement and false vacuum decay on the Potts quantum spin chain

We consider non-equilibrium dynamics after quantum quenches in the mixed-field three-state Potts quantum chain in the ferromagnetic regime. Compared to the analogous setting for the Ising spin chain, the Potts model has a much richer phenomenology, which originates partly from baryonic excitations in the spectrum and partly from the various possible relative alignments of the initial magnetisation and the longitudinal field. We obtain the excitation spectrum by combining semi-classical approximation and exact diagonalisation, and we use the results to explain the various dynamical behaviours we observe. Besides recovering dynamical confinement, as well as Wannier-Stark localisation due to Bloch oscillations similar to the Ising chain, a novel feature is the presence of baryonic excitations in the quench spectroscopy. In addition, when the initial magnetisation and the longitudinal field are misaligned, both confinement and Bloch oscillations only result in partial localisation, with some correlations retaining an unsuppressed light-cone behaviour together with a corresponding growth of entanglement entropy.

cond-mat.stat-mech↗

arXiv2024

Anomalous charge transport in the sine-Gordon model

We conduct a comprehensive study of anomalous charge transport in the quantum sine--Gordon model. Employing the framework of Generalized Hydrodynamics, we compute Drude weights and Onsager matrices across a wide range of coupling strengths to quantify ballistic and diffusive transport, respectively. We find that charge transport is predominantly diffusive at accessible timescales, indicated by the corresponding Onsager matrix significantly exceeding the Drude weight -- contrary to most integrable models where transport is primarily ballistic. Reducing the Onsager matrix to a few key two-particle scattering processes enables us to efficiently examine transport in both low- and high-temperature limits. The charge transport is dictated by non-diagonal scattering of the internal charge degree of freedom: At particular values of the coupling strength with diagonal, diffusive effects amount to merely subleading corrections. However, at couplings approaching these points, the charge Onsager matrix and corresponding diffusive time-scale diverge. Our findings relate to similar transport anomalies in XXZ spin chains, offering insights through their shared Bethe Ansatz structures.

cond-mat.stat-mech↗

arXiv2024

Ginzburg-Landau description for multicritical Yang-Lee models

We revisit and extend Fisher's argument for a Ginzburg-Landau description of multicritical Yang-Lee models in terms of a single boson Lagrangian with potential $φ^2 (i φ)^n$. We explicitly study the cases of $n=1,2$ by a Truncated Hamiltonian Approach based on the free massive boson perturbed by $\boldsymbol P \boldsymbol T$ symmetric deformations, providing clear evidence of the spontaneous breaking of $\boldsymbol P \boldsymbol T$ symmetry. For $n=1$, the symmetric and the broken phases are separated by the critical point corresponding to the minimal model $\mathcal M(2,5)$, while for $n=2$, they are separated by a critical manifold corresponding to the minimal model $\mathcal M(2,5)$ with $\mathcal M(2,7)$ on its boundary. Our numerical analysis strongly supports our Ginzburg-Landau descriptions for multicritical Yang-Lee models.

cond-mat.stat-mech↗

arXiv2024

Dynamical separation of charge and energy transport in one-dimensional Mott insulators

One-dimensional Mott insulators can be described using the sine-Gordon model, an integrable quantum field theory that provides the low-energy effective description of several one-dimensional gapped condensed matter systems, including recent realizations with trapped ultra-cold atoms. Employing the theory of Generalized Hydrodynamics, we demonstrate that this model exhibits separation of the transport of topological charge vs. energy. Analysis of the quasiparticle dynamics reveals that the mechanism behind the separation is the reflective scattering between topologically charged kinks/antikinks. The effect of these scattering events is most pronounced at strong coupling and low temperatures, where the distribution of quasiparticles is narrow compared to the reflective scattering amplitude. This effect results in a distinctively shaped "arrowhead" light cone for the topological charge.

cond-mat.str-el↗

arXiv2024

Non-equilibrium time evolution in the sine-Gordon model revisited

We study the non-equilibrium dynamics of the quantum sine-Gordon model describing a pair of Josephson-coupled one-dimensional bosonic quasi-condensates. Motivated by experimentally accessible quench procedures where the zero mode of the quasi-condensates is weakly coupled to finite momentum modes, we develop a novel Hamiltonian truncation scheme relying on a mini-superspace treatment of the zero mode (MSTHA). We apply this method to simulate the time evolution after both weak and strong quantum quenches, injecting a low or high energy density into the system, and demonstrate that MSTHA accurately captures the dynamics from the hard core boson limit to the experimentally relevant weakly interacting regime for sufficiently mild quenches. In the case of high energy densities, MSTHA breaks down for weak interaction but still extends the range of validity of previous Hamiltonian truncation schemes. We also compare these results to the semiclassical truncated Wigner approximation (TWA) and establish that the dynamics can be well approximated by the semiclassical description in the weakly interacting regime realised in the experiments. In addition, we clarify the importance of the phononic modes depending on the sine-Gordon interaction strength.

cond-mat.stat-mech↗

arXiv2023

PT breaking and RG flows between multicritical Yang-Lee fixed points

We study a novel class of Renormalization Group flows which connect multicritical versions of the two-dimensional Yang-Lee edge singularity described by the conformal minimal models M(2,2n+3). The absence in these models of an order parameter implies that the flows towards and between Lee-Yang edge singularities are all related to the spontaneous breaking of PT symmetry and comprise a pattern of flows in the space of PT symmetric theories consistent with the c-theorem and the counting of relevant directions. Additionally, we find that while in a part of the phase diagram the domains of unbroken and broken PT symmetry are separated by critical manifolds of class M(2,2n+3), other parts of the boundary between the two domains are not critical.

cond-mat.stat-mech↗

arXiv2023

Weak vs. strong breaking of integrability in interacting scalar quantum field theories

The recently proposed classification of integrability-breaking perturbations according to their strength is studied in the context of quantum field theories. Using random matrix methods to diagnose the resulting quantum chaotic behaviour, we investigate the $ϕ^4$ and $ϕ^6$ interactions of a massive scalar, by considering the crossover between Poissonian and Wigner-Dyson distributions in systems truncated to a finite-dimensional Hilbert space. We find that a naive extension of the scaling of crossover coupling with the volume observed in spin chains does not give satisfactory results for quantum field theory. Instead, we demonstrate that considering the scaling of the crossover coupling with the number of particles yields robust signatures, and is able to distinguish between the strengths of integrability breaking in the $ϕ^4$ and $ϕ^6$ quantum field theories.

cond-mat.stat-mech↗

arXiv2023

Thermodynamics and fractal Drude weights in the sine-Gordon model

The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped 1D systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here we fill this gap and derive the framework that captures its thermodynamics and serves as the basis of its hydrodynamic description. As a first application, we compute the Drude weight characterising the ballistic transport of topological charge and demonstrate that its dependence on the value of the coupling shows a fractal structure, similar to the gapless phase of the XXZ spin chain. The thermodynamic framework can be applied to study other features of non-equilibrium dynamics in the sine-Gordon model using generalised hydrodynamics, opening the way to a wide array of theoretical studies and potential novel experimental predictions.

cond-mat.str-el↗

arXiv2023

Multicriticality in Yang-Lee edge singularity

In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin Z2 odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin Z2 even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the conformal non-unitary minimal models M(2,5) and M(2,7) respectively, which is supported by considerations based on PT symmetry and the corresponding extension of Zamolodchikov's c-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [1]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.

hep-th↗

arXiv2022

False vacuum decay in the 1+1 dimensional $φ^4$ theory

The false vacuum is a metastable state that can occur in quantum field theory, and its decay was first studied semi-classically by Coleman. In this work we consider the 1+1 dimensional $φ^4$ theory, which is the simplest model that provides a realisation of this problem. We realise the decay as a quantum quench and study the subsequent evolution using a truncated Hamiltonian approach. In the thin wall limit, the decay rate can be described in terms of the mass of the kink interpolating between the vacua in the degenerate limit, and the energy density difference between the false and true vacuum once the degeneracy is lifted by a symmetry breaking field, a.k.a. the latent heat. We demonstrate that the numerical simulations agree well with the theoretical prediction for several values of the coupling in a range of the value of the latent heat, apart from a normalisation factor which only depends on the interaction strength.

hep-th↗

arXiv2022

Sub-lattice entanglement in an exactly solvable anyon-like spin ladder

We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sub-lattices), such that the scattering phases are constants: particles of the same type scatter as free fermions, whereas the inter-particle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sub-lattice entanglement by numerical means.

cond-mat.stat-mech↗

arXiv2021

Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges in the scaling limit with massive excitations described by the exceptional $E_{8}$ Lie algebra. Using the corresponding analytical form factors of the quantum $E_{8}$ integrable model, we systematically study the spin dynamic structure factor of the perturbed quantum critical Ising chain, where particle channels with total energy up to 5$m_1$ ($m_1$ being the mass of the lightest $E_{8}$ particle) are exhausted. In addition to the significant single-particle contributions to the dynamic spectrum, each two-particle channel with different masses is found to exhibit an edge singularity at the threshold of the total mass and decays with an inverse square root of energy, which is attributed to the singularity of the two-particle density of states at the threshold. The singularity is absent for particles with equal masses due to a cancellation mechanism involving the structure of the form factors. As a consequence, the dynamic structure factor displays a cascade of bumping peaks in the continuum region with clear singular features which can serve as a solid guidance for the material realization of the quantum $E_{8}$ model.

cond-mat.str-el↗

arXiv2019

$T\bar T$-deformation and long range spin chains

We point out that two classes of deformations of integrable models, developed completely independently, have deep connections and share the same algebraic origin. One class includes the $T\bar T$-deformation of 1+1 dimensional integrable quantum field theory and related solvable irrelevant deformations proposed recently. The other class is a specific type of long range integrable deformation of quantum spin chains introduced a decade ago, in the context of $\mathcal{N} = 4$ super-Yang-Mills theory. We show that the detailed structures of the two deformations are formally identical and therefore share many features. Both deformations preserve integrability and lead to non-local deformed theories, resulting in a change of the corresponding factorized S-matrices. We also prove a factorisation formula for the expectation value of the operators which trigger the deformation on the lattice; similar results in quantum field theory play an essential role in the solvability of such deformations. We point out that the long range deformation is a natural counterpart of the $T\bar T$-deformation for integrable spin chains, and argue that this observation leads to interesting new avenues to explore.

hep-th↗

arXiv2019

Perturbative post-quench overlaps in Quantum Field Theory

In analytic descriptions of quantum quenches, the overlaps between the initial pre-quench state and the eigenstates of the time evolving Hamiltonian are crucial ingredients. We construct perturbative expansions of these overlaps in quantum field theories where either the pre-quench or the post-quench Hamiltonian is integrable. Using the $E_8$ Ising field theory for concrete computations, we give explicit expressions for the overlaps up to second order in the quench size, and verify our results against numerical results obtained using the Truncated Conformal Space Approach. We demonstrate that the expansion using the post-quench basis is very effective, but find some serious limitations for the alternative approach using the pre-quench basis.

cond-mat.stat-mech↗

arXiv2019

Hamiltonian truncation approach to quenches in the Ising field theory

In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

cond-mat.stat-mech↗

arXiv2018

Quench dynamics of the Ising field theory in a magnetic field

We numerically simulate the time evolution of the Ising field theory after quenches starting from the $E_8$ integrable model using the Truncated Conformal Space Approach. The results are compared with two different analytic predictions based on form factor expansions in the pre-quench and post-quench basis, respectively. Our results clarify the domain of validity of these expansions and suggest directions for further improvement. We show for quenches in the $E_8$ model that the initial state is not of the integrable pair state form. We also construct quench overlap functions and show that their high-energy asymptotics are markedly different from those constructed before in the sinh/sine-Gordon theory, and argue that this is related to properties of the ultraviolet fixed point.

cond-mat.stat-mech↗