arXiv subjects

Marcin Raczkowski

Publications and source records attributed to Marcin Raczkowski.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet

Low dimensionality enhances quantum fluctuations, triggering novel states of quantum matter to emerge. In real materials, low dimensionality usually arises from spatially strongly anisotropic couplings. Here, we demonstrate a different mechanism: in two-dimensional systems with coupled alternating ferromagnetic (FM) and antiferromagnetic (AFM) spin-$1/2$ chains, an applied magnetic field may drive a dimensional reduction. Under magnetic field, the FM chains polarize and stiffen, suppressing the propagation of transverse AFM fluctuations from one chain to another, and effectively induce one-dimensional behavior at low energies. For a model describing botallackite, Cu$_2$(OH)$_3$Br, quantum Monte Carlo dynamics show that beyond a critical magnetic field, the low-energy spectrum reduces to that of a one-dimensional AFM Heisenberg spin-$1/2$ chain with field-dependent incommensurate two-spinon fluctuations, providing clear signatures for inelastic neutron scattering.

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arXiv2026

Observation of an emergent energy scale close to dimensional reduction in a quasi-two-dimensional quantum magnet

By appropriately perturbing a critical transverse-field Ising chain away from its critical point, the system can develop a finite correlation length with a characteristic purely massive spectrum, whose ratios and correlations are precisely described by an integrable field theory and an infinite set of integrals of motion corresponding to the $E_8$ Lie algebra. In this work, we report on experimental observation of a characteristic massive spectrum close to transverse field-induced dimensional reduction in a quasi-two-dimensional quantum magnet Cu$_2$(OH)$_3$Br, providing evidence for an emergent $E_8$ symmetry and the corresponding excitations of bound states in the sublattice of its ferromagnetic chains. These results demonstrate the power of integrable field theory in describing emergent many-body quantum critical phenomena in condensed matter systems.

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arXiv2026

Revealing altermagnetic Fermi surfaces with two Kondo impurities

Motivated by recent advances in the study of altermagnetism, or unconventional magnetism, and in the realization and manipulation of two-impurity Kondo physics in real materials, we propose a phase-sensitive method to explore unconventional magnetic symmetries. Our method can be implemented with spin-resolved scanning tunneling microscopy to study two-impurity Kondo phenomena on altermagnetic metals by varying the distance and orientation between magnetic impurities. Using quantum Monte Carlo simulations, we analyze the spin splitting of the Kondo resonance, whose spatial distribution sensitively captures the symmetry of the underlying altermagnetic order. Furthermore, the impurity spin correlations reflects the anisotropy of the RKKY interaction due to the altermagnetic Fermi surface splitting. This work provides a framework for studying the competition between the Kondo effect, the RKKY interaction and altermagnetism, in the simplest possible system.

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arXiv2025

Dimensionality-Changing Transition from a Non-Fermi Liquid to a Spin-Solid in a Multichannel Kondo Lattice

A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.

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arXiv2024

Magnetization process of a quasi-two-dimensional quantum magnet: Two-step symmetry restoration and dimensional reduction

We report on a comprehensive thermodynamic study of a quasi-two-dimensional (quasi-2D) quantum magnet Cu$_2$(OH)$_3$Br which in the 2D layer can be viewed as strongly coupled alternating antiferromagnetic and ferromagnetic chains. In an applied magnetic field transverse to the ordered spins below $T_N=9.3$ K, a field-induced phase transition from the 3D ordered to a disordered phase occurs at $B_c=16.3$ T for the lowest temperature, which is featured by an onset of a one-half plateau-like magnetization. By performing quantum Monte Carlo simulations of the relevant 2D model, we find that the plateau-like magnetization corresponds to a partial symmetry restoration and the full polarization in the ferromagnetic chains. Our numerical simulations also show that the magnetization saturation occurs with full symmetry restoration at a much higher field of $B_s \simeq 95$ T, corresponding to a 1D quantum phase transition in the antiferromagnetic chains. We argue that the experimentally observed field-induced phase transition at $B_c$ follows from the partial symmetry restoration and the concomitant dimensional reduction.

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arXiv2024

Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment

Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this study, we formulate a set of models of Dirac fermions in 2+1 dimensions with SU($N$)$\times$SU(2)$\times$U(1) symmetry that have the potential to host critical points described by field theories with topological terms. For $N=2$ it shows a rich phase diagram containing semimetallic, quantum spin Hall insulating, Kekul\'e valence bond solid and s-wave superconducting phases and features multiple Landau-Ginzburg-Wilson phase transitions driven by interaction strength. At $N=1$ a deconfined quantum critical point is observed. At $N=2$ one expects the critical theory to correspond to a level 2 Wess-Zumino-Witten theory in 2+1 dimensions. Here the numerical results however show a strong first order transition. Another transition can be governed by a topological $\theta$-term which is rendered irrelevant for even values of $N$ thus leading to Landau-Ginzburg-Wilson behaviour.

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arXiv2024

SU($\boldsymbol N$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order

We map out the ground state phase diagram of a one-dimensional SU($N$) Kondo-Heisenberg lattice model at half filling and in the fully antisymmetric self-adjoint representation as a function of $\tfrac {1}{N}$ and Kondo coupling $J_k/t$. On the basis of auxiliary field quantum Monte Carlo (QMC) simulations with even $N$ up to 8, we show that the enlarged SU($N\ge 4$) symmetry realizes a quantum phase transition separating a valence bond solid (VBS) phase occupying a weak coupling part of the phase diagram and the Kondo insulator (KI) state dominating in the strong $J_k/t$ limit. Along the phase boundary, we always observe critical exponents that belong to a two-dimensional classical Ising universality class. We next trace the evolution of the composite fermion and spin spectral functions across the phase boundary and conclude that VBS order triggers a bond order wave state of conduction electrons, both coexisting with Kondo screening. Upon further reducing $J_k/t$ we observe that composite quasiparticles lose their spectral weight indicating that VBS order gradually liberates localized $f$ spins from forming Kondo singlets with conduction electron spins. We contrast the QMC results with a static large-$N$ approximation, and we show that in the limit of infinite degeneracy $N\to\infty$ the order-disorder transition becomes of first order and is accompanied by a full decoupling of conduction electrons and localized $f$ spins. We complete our analysis by considering the limit of a vanishing Heisenberg coupling $J_h=0$, and we provide evidence that the enlarged SU($N$) symmetry and low dimensionality of the RKKY exchange interaction are not sufficient to induce VBS order in the conventional SU($N$) Kondo chain which hosts solely a KI phase.

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arXiv2022

Breakdown of heavy quasiparticles in a honeycomb Kondo lattice: A quantum Monte Carlo study

We show that for the half-filled Kondo lattice model on the honeycomb lattice a Kondo breakdown occurs at small Kondo couplings $J_k$ within the magnetically ordered phase. Our conclusions are based on auxiliary field quantum Monte Carlo simulations of the so-called composite fermion spectral function. Within a U(1) gauge theory formulation of the Kondo model, it becomes apparent that a Higgs mechanism dictates the weight of the resonance in the spectral function. For the honeycomb lattice we observe that for small $J_k$ the quasiparticle pole gives way to incoherent spectral weight but it remains well defined for the square lattice. Our result provides an explicit example where the magnetic transition and the breakdown of heavy quasiparticles are detached as observed in Yb(Rh$_{0.93}$Co$_{0.07}$)$_2$Si$_2$ [Friedemann et al., Nat. Phys. \textbf{5}, 465 (2009)].

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arXiv2021

Zooming in on heavy fermions in Kondo lattice models

Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as $e^{-W/J_k}$ with $W$ the bandwidth and $J_k$ the Kondo coupling, the residue of the composite fermion tracks $J_k$. This result holds down to $J_k/W = 0.05$, and confirms the point of view that magnetic ordering, present below $J_k/W = 0.18$, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for SU($N$) generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-$N$, large-$S$, and large $J_k$. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.

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arXiv2021

Local moments versus itinerant antiferromagnetism: magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model

Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain $t$ and interchain $t_{\perp}$ hopping amplitudes at half-filling. A fixed value of the next-nearest-neighbor hopping $t'=-t_{\perp}/2$ removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime $t_{\perp}/t\lesssim 0.3$ displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.

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arXiv2020

The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations

We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function -- \textit{waterfall} features and narrow spin-polaron bands -- is only visible in the lattice QMC approach.

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arXiv2020

Phase diagram and dynamics of the SU($\boldsymbol N$) symmetric Kondo lattice model

In heavy-fermion systems, the competition between the local Kondo physics and intersite magnetic fluctuations results in unconventional quantum critical phenomena which are frequently addressed within the Kondo lattice model (KLM). Here we study this interplay in the SU($N$) symmetric generalization of the two-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ up to 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spin systems typically gives way to spin-singlet ground states with spontaneously broken lattice symmetry, we find that the SU($N$) KLM is unique in that for each finite $N$ its ground-state phase diagram hosts only two phases -- AF order and the Kondo-screened phase. The absence of any intermediate phase between the $N=2$ and large-$N$ cases establishes adiabatic correspondence between both limits and confirms that the large-$N$ theory is a correct saddle point of the KLM fermionic path integral and a good starting point to include quantum fluctuations. In addition, we determine the evolution of the single-particle gap, quasiparticle residue of the doped hole at momentum $(π,π)$, and spin gap across the magnetic order-disorder transition. Our results indicate that increasing $N$ modifies the behavior of the coherence temperature: while it evolves smoothly across the magnetic transition at $N=2$ it develops an abrupt jump -- of up to an order of magnitude -- at larger but finite $N$. We discuss the magnetic order-disorder transition from a quantum-field-theoretic perspective and comment on implications of our findings for the interpretation of experiments on quantum critical heavy-fermion compounds.

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arXiv2019

Emergent Coherent Lattice Behavior in Kondo Nanosystems

How many magnetic moments periodically arranged on a metallic surface are needed to generate a coherent Kondo lattice behavior? We investigate this fundamental issue within the particle-hole symmetric Kondo lattice model using quantum Monte Carlo simulations. Extra magnetic atoms forming closed shells around the initial impurity induce a fast splitting of the Kondo resonance at the inner shells which signals the formation of composite heavy-fermion bands. The onset of the hybridization gap matches well the enhancement of antiferromagnetic spin correlations in the plane perpendicular to the applied magnetic field, a genuine feature of the coherent Kondo lattice. In contrast, the outermost shell remains dominated by a local Kondo physics with spectral features resembling the single-impurity behavior.

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arXiv2017

Interplay between the edge-state magnetism and long-range Coulomb interaction in zigzag graphene nanoribbons: quantum Monte Carlo study

We perform projective quantum Monte Carlo simulations of zigzag graphene nanoribbons within a realistic model with long-range Coulomb interactions. Increasing the relative strength of nonlocal interactions with respect to the on-site repulsion does not generate a phase transition but has a number of nontrivial effects. At the single-particle level we observe a marked enhancement of the Fermi velocity at the Dirac points. At the two-particle level, spin- and charge-density-wave fluctuations compete. As a consequence, the edge magnetic moment is reduced but the edge dispersion relation increases in the sense that the single-particle gap at momentum $q=π/|{\pmb a}_1|$ grows. We attribute this to nonlocal charge fluctuations which assist the spin fluctuations to generate the aforementioned gap. In contrast, the net result of the interaction-induced renormalization of different energy scales is a constant spin-wave velocity of the edge modes. However, since the particle-hole continuum is shifted to higher energies---due to the renormalization of the Fermi velocity---Landau damping is reduced. As a result, a roughly linear spin-wave-like mode at the edge spreads out through a larger part of the Brillouin zone.

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arXiv2016

Mott Quantum Criticality in the Anisotropic 2D Hubbard Model

We present evidence for Mott quantum criticality in an anisotropic two-dimensional system of coupled Hubbard chains at half-filling. In this scenario emerging from variational cluster approximation and cluster dynamical mean-field theory, the interchain hopping $t_{\perp}$ acts as a control parameter driving the second-order critical end point $T_c$ of the metal-insulator transition down to zero at $t_{\perp}^{c}/t\simeq 0.2$. Below $t_{\perp}^{c}$, the volume of the hole and electron Fermi pockets of a compensated metal vanishes continuously at the Mott transition. Above $t_{\perp}^{c}$, the volume reduction of the pockets is cut off by a first-order transition. We discuss the relevance of our findings to a putative quantum critical point in layered organic conductors, whose location remains elusive so far.

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arXiv2015

Spin and charge dynamics of a quasi-one-dimensional antiferromagnetic metal

We use quantum Monte Carlo simulations to study a finite-temperature dimensional-crossover-driven evolution of spin and charge dynamics in weakly coupled Hubbard chains with a half-filled band. The low-temperature behavior of the charge gap indicates a crossover between two distinct energy scales: a high-energy one-dimensional (1D) Mott gap due to the umklapp process and a low-energy gap which stems from long-range antiferromagnetic (AF) fluctuations. Away from the 1D regime and at temperature scales above the charge gap, the emergence of a zero-frequency Drude-like feature in the interchain optical conductivity $σ_{\perp}(ω)$ implies the onset of a higher-dimensional metal. In this metallic phase, enhanced quasiparticle scattering off finite-range AF fluctuations results in incoherent single-particle dynamics. The coupling between spin and charge fluctuations is also seen in the spin dynamical structure factor $S({\pmb q},ω)$ displaying damped spin excitations (paramagnons) close to the AF wave-vector ${\pmb q}=(π,π)$ and particle-hole continua near 1D momentum transfers spanning quasiparticles at the Fermi surface. We relate our results to the charge deconfinement in quasi-1D organic Bechgaard-Fabre salts.

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arXiv2013

Spinon confinement: dynamics of weakly coupled Hubbard chains

Using large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half-filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at $T=0$. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.

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arXiv2012

Dimensional-crossover-driven Mott transition in the frustrated Hubbard model

We study the Mott transition in a frustrated Hubbard model with next-nearest neighbor hopping at half-filling. The interplay between interaction, dimensionality and geometric frustration closes the one-dimensional Mott gap and gives rise to a metallic phase with Fermi surface pockets. We argue that they emerge as a consequence of remnant one-dimensional Umklapp scattering at the momenta with vanishing interchain hopping matrix elements. In this pseudogap phase, enhanced d-wave pairing correlations are driven by antiferromagnetic fluctuations. Within the adopted cluster dynamical mean-field theory on the $8\times 2$ cluster and down to our lowest temperatures the transition from one to two dimensions is continuous.

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