arXiv subjects

Pawel Jakubczyk

Publications and source records attributed to Pawel Jakubczyk.

At least 19 recordsLinked to original sources

arXiv2026

Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective

We develop a theoretical framework based on the nonperturvative renormalization group (RG) in the one-particle irreducible (Wetterich) formulation to tackle the interplay of coupled fermionic and order-parameter fluctuations at metallic quantum critical points (QCPs) with ordering wavevector $\vec{Q}=\vec{0}$. We consistently treat the dynamical emergence of the Landau damping of the bosonic mode and non-Fermi liquid scaling of fermions upon lowering the cutoff scale. The loop integrals of the present theory involve only contributions from fluctuations above the cutoff scale, which protects the system from developing singular bosonic interactions. We emphasize the importance of the nontrivial relative scaling of the bosonic and fermionic cutoffs $Λ$ and $Λ_f$, which we fix by analyzing the RG flow of the scale-dependent ordering wave-vector $\vec{Q}_Λ$. Upon neglecting Fermi self-energy in the loop integrals of the functional RG flow, we identify a non-Fermi liquid RG fixed point and recover the features obtained earlier within RPA-type approaches. In a subsequent step, we self-consistently include the scaling of the self-energy and the Yukawa coupling. We find a generic instability of the non-Fermi liquid RG fixed point. This implies, at least at this truncation level, absence of the QCP with $\vec{Q}=\vec{0}$ and development of a first-order phase transition or a phase characterized by $\vec{Q}\neq\vec{0}$.

cond-mat.str-el↗

arXiv2026

Phase diagram of two-component mean-field Bose mixtures

We revisit the structure of the phase diagram of the two-component mean-field Bose mixture at finite temperatures, considering both the cases of attractive and repulsive interspecies interactions. In particular, we analyze the evolution of the phase diagram upon driving the system towards collapse and point out its distinctive features in this limit. We provide analytical insights into the global structure of the phase diagram and the properties of the phase transitions between the normal phase and the phases involving Bose-Einstein condensates. \emph{Inter alia} we analytically demonstrate that for sufficiently weak interspecies interactions $a_{12}$ the system generically exhibits a line of quadruple points but has no triple nor tricritical points in the phase diagram spanned by the chemical potentials $μ_1$, $μ_2$ and temperature $T$. In contrast, for sufficiently large, positive values of $a_{12}$, the system displays both triple and tricritical points but no quadruple points. As pointed out in recent studies, in addition to the phase transitions involving condensation, the mixture may be driven through a liquid-gas type transition, and we clarify the conditions for its occurrence. We finally discuss the impact of interaction- and mass-imbalance on the phase diagram of the mixture.

cond-mat.stat-mech↗

arXiv2025

Anisotropic scale invariance and the uniaxial Lifshitz point from the nonperturbative renormalization group

We employ the derivative expansion of the nonperturbative renormalization group to address the phenomenon of anisotropic scale invariance and the associated functional fixed points, also known as Lifshitz points, in systems characterized by a scalar order parameter. We demonstrate the existence of the Lifshitz fixed point featuring a non-classical value of the anisotropy exponent $θ<1/2$ and provide estimates for values of a set of critical exponents in the physically most relevant case of the three-dimensional uniaxial Lifshitz point $(d,m)=(3,1)$, $m$ denoting the anisotropy index. We compare our predictions with existing estimates from perturbative expansions around dimensionality $d=4+\frac{1}{2}$ as well as those from the $1/N$ expansion.

cond-mat.stat-mech↗

arXiv2025

Thermal Casimir effect in the spin-orbit coupled Bose gas

We study the thermal Casimir effect in ideal Bose gases with spin-orbit (S-O) coupling of Rashba type below the critical temperature for Bose-Einstein condensation. In contrast to the standard situation involving no S-O coupling, the system exhibits long-ranged Casimir forces both in two and three dimensions ($d=2$ and $d=3$). We identify the relevant scaling variable involving the ratio $D/ν$ of the separation between the confining walls $D$ and the S-O coupling magnitude $ν$. We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases the resulting Casimir force is attractive and the S-O coupling $ν$ has impact on its magnitude. In $d=3$ the exponent governing the decay of the Casimir force becomes modified by the presence of the S-O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In $d=2$ the obtained Casimir force displays singular behavior in the limit of vanishing $ν$

cond-mat.quant-gas↗

arXiv2024

Spin-orbit coupled mean-field Bose gas at finite temperature

We consider the spin-orbit coupled Bose gas with repulsive mean-field interparticle interactions. We analyze the phase diagram of the system varying the temperature $T>0$, the chemical potentials, as well as interparticle and spin-orbit interaction couplings. Our results indicate that, for Rashba- and Weyl-type spin-orbit couplings, condensates featuring ordering wavevector $\vec{Q}\neq \vec{0}$ are fragile with respect to thermal fluctuations and, at $T>0$, the only stable thermodynamic phases involving the Bose-Einstein condensate (BEC) are those of uniform type with $\vec{Q}=\vec{0}$. On the other hand, presence of the spin-orbit coupling stabilizes the $\vec{Q}=\vec{0}$ BEC state at any dimensionality $d>1$ and modifies either the order or the universality class of the corresponding phase transition. We emphasize the singular nature of the limit of vanishing spin-orbit interaction coupling $v$, sizable shifts of the phase boundaries upon varying $v$, as well as the role of the relative magnitudes of the interparticle interaction couplings for the character of the condensation transition.

cond-mat.quant-gas↗

arXiv2023

First-order, continuous, and multicritical Bose-Einstein condensation in Bose mixtures

We address the possibility of realizing Bose-Einstein condensation as a first-order phase transition by admixture of particles of different species. To this aim we perform a comprehensive analysis of phase diagrams of two-component mixtures of bosons at finite temperatures. As a prototype model, we analyze a binary mixture of Bose particles interacting via an infinite-range (Kac-scaled) two-body potential. We obtain a rich phase diagram, where the transition between the normal and Bose-Einstein condensed phases may be either continuous or first-order. The phase diagram hosts lines of triple points, tricritical points, as well as quadruple points. We address the structure of the phase diagram depending on the relative magnitudes of the inter- and intra-species interaction couplings. In addition, even for purely repulsive interactions, we identify a first-order liquid-gas type transition between non-condensed phases characterized by different particle concentrations. In the obtained phase diagram, a surface of such first-order transitions terminates with a line of critical points.

cond-mat.quant-gas↗

arXiv2022

$\mathbb{Z}_4$-symmetric perturbations to the XY model from functional renormalization

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic ($\mathbb{Z}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide accurate estimates of the eigenvalue $y_4$ corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from $d=3$ towards $d=2$, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to $O(2)$-symmetric and $\mathbb{Z}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.

cond-mat.stat-mech↗

arXiv2021

Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

We revisit the question concerning stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. Invoking the properties of the putative phase diagram of two-component Fermi mixtures, on general grounds we argue, that for isotropic, continuum systems the phase diagram hosting a long-range-ordered FFLO-type phase envisaged by the mean-field theory cannot be stable to fluctuations at any temperature $T>0$ in any dimensionality $d<4$. In contrast, in layered unidirectional systems the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at $T>0$ is $d=5/2$. In consequence, its occurrence is excluded in $d=2$, but not in $d=3$. We propose a relatively simple method, based on nonperturbative renormalization group to compute the critical exponents of the thermal $m$-axial Lifshitz point continuously varying $m$, spatial dimensionality $d$ and the number of order parameter components $N$. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.

cond-mat.quant-gas↗

arXiv2021

Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality

We analyze the thermodynamic Casimir effect occurring in a gas of non-interacting bosons confined by two parallel walls with a strongly anisotropic dispersion inherited from an underlying lattice. In the direction perpendicular to the confining walls the standard quadratic dispersion is replaced by the term $|{\bf p}|^α$ with $α\geq 2$ treated as a parameter. We derive a closed, analytical expression for the Casimir force depending on the dimensionality $d$ and the exponent $α$, and analyze it for thermodynamic states in which the Bose-Einstein condensate is present. For $α\in\{4,6,8,\dots\}$ the exponent governing the decay of the Casimir force with increasing distance between the walls becomes modified and the Casimir amplitude $Δ_α(d)$ exhibits oscillations of sign as a function of $d$. Otherwise we find that $Δ_α(d)$ features singularities when viewed as a function of $d$ and $α$. Recovering the known previous results for the isotropic limit $α=2$ turns out to occur via a cancellation of singular terms.

cond-mat.quant-gas↗

arXiv2021

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

We employ the functional renormalization group framework at the second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $ν$ and $η$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $η(d,N)$ and $ν^{-1}(d,N)$ as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the $(d,N)$ plane, however no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $η(d,N)$ and $ν^{-1}(d,N)$ become increasingly large for $d\to 2$ and $N\to 2$ and it is only in this limit that $η(d,N)$ and $ν^{-1}(d,N)$ as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on $N$ for $d>2$ we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality $d$ approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

cond-mat.stat-mech↗

arXiv2020

Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures

We perform a detailed analysis of the phase transition between the uniform superfluid and normal phases in spin- and mass-imbalanced Fermi mixtures. At mean-field level we demonstrate that at temperature $T\to 0$ the gradient term in the effective action can be tuned to zero for experimentally relevant sets of parameters, thus providing an avenue to realize a quantum Lifshitz point. We subsequently analyze damping processes affecting the order-parameter field across the phase transition. We show that, in the low energy limit, Landau damping occurs only in the symmetry-broken phase and affects exclusively the longitudinal component of the order-parameter field. It is however unavoidably present in the immediate vicinity of the phase transition at temperature $T=0$. We subsequently perform a renormalization-group analysis of the system in a situation, where, at mean-field level, the quantum phase transition is second order (and not multicritical). We find that, at $T$ sufficiently low, including the Landau damping term in a form derived from the microscopic action destabilizes the renormalization group flow towards the Wilson-Fisher fixed point. This signals a possible tendency to drive the transition weakly first-order by the coupling between the order-parameter fluctuations and fermionic excitations effectively captured by the Landau damping contribution to the order-parameter action.

cond-mat.quant-gas↗

arXiv2019

Damping of the Anderson-Bogolyubov mode by spin and mass imbalance in Fermi mixtures

We study the temporally nonlocal contributions to the gradient expansion of the pair fluctuation propagator for spin- and mass-imbalanced Fermi mixtures. These terms are related to damping processes of sound-like (Anderson-Bogolyubov) collective modes and are relevant for the structure of the complex pole of the pair fluctuation propagator. We derive conditions under which damping occurs even at zero temperature for large enough mismatch of the Fermi surfaces. We compare our analytical results with numerically computed damping rates of the Anderson-Bogolyubov mode.

cond-mat.quant-gas↗

arXiv2019

Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization

We study the $O(2)$ model with $\mathbb{Z}_4$-symmetric perturbations within the framework of nonperturbative renormalization group (RG) for spatial dimensionality $d=2$ and $d=3$. In a unified framework we resolve the relatively complex crossover behavior emergent due to the presence of multiple RG fixed points. In $d=3$ the system is controlled by the $XY$, Ising, and low-$T$ fixed points in presence of a dangerously irrelevant anisotropy coupling $λ$. In $d=2$ the anisotropy coupling is marginal and the physical picture is governed by the interplay between two distinct lines of RG fixed points, giving rise to nonuniversal critical behavior; and an isolated Ising fixed point. In addition to inducing crossover behavior in universal properties, the presence of the Ising fixed point yields a generic, abrupt change of critical temperature at a specific value of the anisotropy field.

cond-mat.stat-mech↗

arXiv2018

Effective potential and quantum criticality for imbalanced Fermi mixtures

We study the analytical structure of the effective action for spin- and mass-imbalanced Fermi mixtures at the onset of the superfluid state. Of our particular focus is the possibility of suppressing the tricritical temperature to zero, so that the transition remains continuous down to $T=0$ and the phase diagram hosts a quantum critical point. At mean-field level we analytically identify such a possibility in a regime of parameters in dimensionality $d=3$. In contrast, in $d=2$ we demonstrate that the occurrence of a quantum critical point is (at the mean-field level) excluded. We show that the Landau expansion of the effective potential remains well-defined in the limit $T\to 0^+$ except for a subset of model parameters which includes the standard BCS limit. We calculate the mean-field asymptotic shape of the transition line. Employing the functional renormalization group framework we go beyond the mean field theory and demonstrate the stability of the quantum critical point in $d=3$ with respect to fluctuations.

cond-mat.quant-gas↗

arXiv2018

Phase diagram and correlation functions of the anisotropic imperfect Bose gas in $d$ dimensions

We study an anisotropic variant of the $d$-dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion $ε_{\bf k}$ at vanishing momentum $\bf{k}$ may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent $ψ$ governing the asymptotic behaviour of the critical temperature $T_c(μ)$ as a function of the chemical potential $μ$ at $T_c\to 0$. We argue that the universality classes of Bose-Einstein condensation admitted by the model may be classified according to the allowed values of $ψ$ so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function $χ({\bf x})$ at $T>T_c$ turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of ${\bf x}$ with respect to the dispersion anisotropies.

cond-mat.stat-mech↗

arXiv2017

Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at $T>0$

Within the renormalization group framework we study the stability of superfluid density wave states, known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with respect to thermal order-parameter fluctuations in two and three-dimensional ($d\in \{2,3\}$) systems. We analyze the renormalization-group flow of the relevant ordering wave-vector $\vec{Q_0}$. The calculation indicates an instability of the FFLO-type states towards either a uniform superfluid or the normal state in $d\in\{2,3\}$ and $T>0$. In $d=2$ this is signaled by $\vec{Q_0}$ being renormalized towards zero, corresponding to the flow being attracted either to the usual Kosterlitz-Thouless fixed-point or to the normal phase. We supplement a solution of the RG flow equations by a simple scaling argument, supporting the generality of the result. The tendency to reduce the magnitude of $\vec{Q_0}$ by thermal fluctuations persists in $d=3$, where the very presence of long-range order is immune to thermal fluctuations, but the effect of attracting $\vec{Q_0}$ towards zero by the flow remains observed at $T>0$.

cond-mat.quant-gas↗

arXiv2017

Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase

We analyze the interplay of longitudinal and transverse fluctuations in a $U(1)$ symmetric two-dimensional $ϕ^4$-theory. To this end, we derive coupled renormalization group equations for both types of fluctuations obtained from a linear (cartesian) decomposition of the order parameter field. Discarding the longitudinal fluctuations, the expected Berezinskii-Kosterlitz-Thouless (BKT) phase characterized by a finite stiffness and an algebraic decay of order parameter correlations is recovered. Renormalized by transverse fluctuations, the longitudinal mass scales to zero, so that longitudinal fluctuations become increasingly important for small momenta. Within our expansion of the effective action, they generate a logarithmic decrease of the stiffness, in agreement with previous functional renormalization group calculations. The logarithmic terms imply a deviation from the vanishing beta-function for the stiffness in the non-linear sigma model describing the phase fluctuations at three-loop order. To gain further insight, we also compute the flow of the parameters characterizing longitudinal and transverse fluctuations from a density-phase representation of the order parameter field, with a cutoff on phase fluctuations. The power-law flow of the longitudinal mass and other quantities is thereby confirmed, but the stiffness remains finite in this approach. We conclude that the marginal flow of the stiffness obtained in the cartesian representation is an artifact of the truncated expansion of momentum dependences.

cond-mat.stat-mech↗

arXiv2016

Thermodynamics of the two-dimensional XY model from functional renormalization

We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $ϕ^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.

cond-mat.stat-mech↗