arXiv subjects

Dirk Schuricht

Publications and source records attributed to Dirk Schuricht.

At least 19 recordsLinked to original sources

arXiv2026

Universal correlations in the Abelian sandpile model

We numerically study the bulk correlation functions in the two-dimensional Abelian sandpile model, aiming both to compare with the predictions of logarithmic conformal field theory and to extend the analysis to lattices where analytical methods are difficult to apply. Wilson's algorithm efficiently generates large-scale uniform spanning trees in parallel, which can be mapped to independent recurrent configurations via the Majumdar--Dhar burning bijection, eliminating sample autocorrelations and yielding fast convergence. On the square (single-sublattice) and honeycomb (two-sublattice) lattices our results agree well with the analytical predictions. For the kagome lattice we provide the first systematic numerical study of the bulk correlation functions, and cross-check the bulk height-1 probability against a closed-form analytical expression that we also derive here via the lattice Green function.

math-ph↗

arXiv2026

Hall viscosity and putative quantum Hall states without positive-definite K-matrix

We investigate putative quantum Hall effect states, labeled by their K-matrix equal to (1 1 3), by defining them on the torus and computing their Hall viscosity. Such states have been introduced on the sphere as a phase distinct from Pfaffian and anti-Pfaffian ones. This was done in order to explain certain results on thermal Hall conductivity in favor of particle-hole symmetric Pfaffian topological order in presence of Landau level mixing. The requirements of boundary conditions, modular invariance and ground state degeneracy are enough to uniquely fix the form of the proposed wave functions. We generalize a method to enforce them which we call monodromy matching and check our results on wave functions and Hall viscosity against realizations on the torus of Laughlin and hierarchical states. We highlight the issues in the realization of these states, which turn out to exhibit the formation of clusters. We show that the effect of anti-symmetrization on the system is not enough to prevent clustering; we compute the Hall viscosity for the Halperin version of these states and the fully anti-symmetrized one and we find them being dependent on the geometry and the particle number.

cond-mat.str-el↗

arXiv2026

Wick theorem for analytic functions of Gaussian fields

We compute the correlation of analytic functions of general Gaussian fields in terms of multigraphs and Feynman diagrams on the lattice Z^d. Then, we connect its scaling limit to tensors of the correlation functionals of Fock space fields. Afterwards, we investigate the relation with fermionic Gaussian field states for even functions. For instance, we characterize the correlation functionals of the exponential of a continuous Gaussian Free Field or general analytic functions of fractional Gaussian fields as limits of quantities constructed via a sequences of discrete fields. Finally, we show that the duality between even powers of bosonic Gaussian fields and "complex" fermionic Gaussian fields can be reformulated in terms of a principal minors assignment problem of the corresponding covariance matrices.

math.PR↗

arXiv2026

Inefficiency of the block approximation in diploid Probabilistic Cellular Automata

We study a probabilistic cellular automaton obtained as a mixture of the additive elementary rules 60 and 102. We prove that, for any finite periodic lattice and for mixing parameter $λ=1/2$, the system almost surely reaches the absorbing all-zero configuration in finitely many steps. In addition, Monte Carlo simulations indicate as well the presence of a zero-density stationary state in a finite interval around $λ=1/2$. Despite this absorbing behavior, both mean-field and block approximation schemes predict a stationary state with non-zero density. This failure, traced to the additive and mirror symmetries of the deterministic components, highlights a fundamental limitation of finite-block approximation in capturing the global dynamics of probabilistic cellular automata.

nlin.CG↗

arXiv2026

Quantum typicality approach to energy flow between two spin-chain domains at different temperatures

We discuss a quantum typicality approach to examine systems composed of two subsystems at different temperatures. While dynamical quantum typicality is usually used to simulate high-temperature dynamics, we also investigate low-temperature dynamics using the method. To test our method, we investigate the energy current between subsystems at different temperatures in various paradigmatic spin-1/2 chains, specifically the XX chain, the critical transverse-field Ising chain, and the XXZ chain. We compare our numerics to existing analytical results and find a convincing agreement for the energy current in the steady state for all considered models and temperatures.

cond-mat.stat-mech↗

arXiv2025

A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain

We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G$_2$. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G$_2$ analog of the famous AKLT chain.

cond-mat.str-el↗

arXiv2024

Relaxation dynamics of integrable field theories after a global quantum quench

We apply the linked cluster expansion as well as the quench action approach to study the time evolution of one-point functions after a quantum quench in integrable field theories. We argue that the relaxation towards the stationary value fundamentally differs depending on the locality properties of the considered observable: while for local operators both exponential and power-law decaying terms are present in the dynamics, for semi-local operators the latter are absent. We explicitly confirm this for the Ising field theory, the sinh-Gordon model, and the repulsive sine-Gordon model.

cond-mat.str-el↗

arXiv2023

Quantum quenches in the sinh-Gordon and Lieb-Liniger models

The non-relativistic limit of integrable field theories at equilibrium has been intensively studied in the previous years; the simplest non-trivial case relates the sinh-Gordon model to the Lieb-Liniger model. Here we study this non-relativistic limit out of equilibrium, namely in the time evolution after a quantum quench. The obtained results agree with the known ones for the Lieb-Liniger model, thus showing that the non-relativistic limit is applicable in this out-of-equilibrium setting.

cond-mat.str-el↗

arXiv2023

$G_2$ Integrable Point Characterization via Isotropic Spin-3 Chains

We investigate the physical properties of $G_2$-symmetric integrable chains with local degrees of freedom in the fundamental representation; given the typical connection between integrability and critical points, we test the model's properties against a hypothesis of conformal-invariant long-distance behavior. Leveraging an embedding between the $G_2$ exceptional Lie algebra and $SU(2)$-symmetric chains with local spin-3 representations, we perform numerical analyses via exact diagonalization (ED) targeted at specific spin sectors, as well as via non-Abelian density-matrix renormalization group (DMRG). A basic study of the momentum-resolved ED spectrum suggests the low-energy system is effectively described by a $(G_2)_1$ Wess--Zumino--Witten (WZW) theory, but we find challenges in further numerical characterization of conformal data. The study and control of the phenomenology of this model may have implications for the development of accessible models for Fibonacci anyons.

cond-mat.str-el↗

arXiv2023

Exact ground states for interacting Kitaev chains

We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly degenerate ground states even for finite system sizes. We present analytical results for the strong Majorana zero modes, the phase diagram and the topological order. Furthermore, we generalise our results to include interactions.

cond-mat.str-el↗

arXiv2022

Interrelations among frustration-free models via Witten's conjugation

We apply Witten's conjugation argument [Nucl. Phys. B 202, 253 (1982)] to spin chains, where it allows us to derive frustration-free systems and their exact ground states from known results. We particularly focus on $\mathbb{Z}_p$-symmetric models, with the Kitaev and Peschel--Emery line of the axial next-nearest neighbour Ising (ANNNI) chain being the simplest examples. The approach allows us to treat two $\mathbb{Z}_3$-invariant frustration-free parafermion chains, recently derived by Iemini et al. [Phys. Rev. Lett. 118, 170402 (2017)] and Mahyaeh and Ardonne [Phys. Rev. B 98, 245104 (2018)], respectively, in a unified framework. We derive several other frustration-free models and their exact ground states, including $\mathbb{Z}_4$- and $\mathbb{Z}_6$-symmetric generalisations of the frustration-free ANNNI chain.

cond-mat.str-el↗

arXiv2022

Lower bounds for Ramsey numbers as a statistical physics problem

Ramsey's theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this abstract setting and a statistical physics problem. Specifically, we design a classical Hamiltonian that favours configurations in a way to establish lower bounds on Ramsey numbers. As a proof of principle we then use Monte Carlo methods to obtain such lower bounds, finding rough agreement with known literature values in a few cases we investigated. We discuss numerical limitations of our approach and indicate a path towards the treatment of larger graph sizes.

math.CO↗

arXiv2022

Phase diagram of an extended parafermion chain

We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral $\mathbb{Z}_3$ axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.

cond-mat.str-el↗

arXiv2021

The quantum sine-Gordon model with quantum circuits

Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions for one of the paradigmatic models of an integrable quantum field theory: the quantum sine-Gordon (qSG) model in 1+1 space-time dimensions. We analyze the lattice model using the density matrix renormalization group technique and benchmark our numerical results with existing Bethe ansatz computations. Furthermore, we perform analytical form-factor calculations for the two-point correlation function of vertex operators, which closely agree with our numerical computations. Finally, we compute the entanglement spectrum of the qSG model. We compare our results with those obtained using the integrable lattice-regularization based on the quantum XYZ chain and show that the quantum circuit model is less susceptible to corrections to scaling compared to the XYZ chain. We provide numerical evidence that the parameters required to realize the qSG model are accessible with modern-day superconducting circuit technology, thus providing additional credence towards the viability of the latter platform for simulating strongly interacting quantum field theories.

quant-ph↗

arXiv2021

Intersublattice entanglement entropy as an extensive property in antiferromagnets

Recent advancements in our understanding of ordered magnets call for a quantification of their entanglement content on an equal footing with classical thermodynamic quantities, such as the total magnetic moment. We evaluate the entanglement entropy (EE) between the two sublattices of a bipartite ordered antiferromagnet finding it to scale with volume. Thus, the EE density becomes an intensive property and is evaluated to be a universal dimensionality-dependent constant when exchange is the dominant interaction. Our analytic results are validated against the DMRG-based analysis of a one-dimensional (1D) system, finding good agreement. Further, our evaluated EE per bond provides a useful shortcut towards obtaining the central-cut EE in 1D, and the area law in higher-dimensional magnets.

cond-mat.mes-hall↗

arXiv2020

Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

We study a tight binding model of $\mathbb{Z}_3$-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

cond-mat.str-el↗

arXiv2020

Energy transport between critical one-dimensional systems with different central charges

Energy transport can reveal information about interacting many-body systems beyond other transport probes. In particular, in one dimension it has been shown that the energy current is directly proportional to the central charge, thus revealing information about the degrees of freedom of critical systems. In this work, we explicitly verify this result in two cases for translationally invariant systems based on explicit microscopic calculations. More importantly, we generalise the result to non-translation invariant setups and use this to study a composite system of two subsystems possessing different central charges. We find a bottleneck effect meaning the smaller central charge limits the energy transport.

cond-mat.str-el↗

arXiv2019

Finite-time quantum quenches in the XXZ Heisenberg chain

We study the time evolution of the two-point correlation functions in the XXZ Heisenberg chain after a finite-time quantum quench in the anisotropy. We compare results from numerical simulations to ones obtained in the Luttinger model and find good agreement. We analyse the spreading of the correlations and the associated light-cone features. We observe a delay in the appearance of the light cone as compared to the sudden-quench setup, and link this delay to the properties of the quench protocol.

cond-mat.str-el↗