arXiv subjects

Abay Zhakenov

Publications and source records attributed to Abay Zhakenov.

10 recordsLinked to original sources

arXiv2026

Monotonic and non-Nonmonotonic Impurity Entropy flows in a $\mathscr{PT}$-Symmetric Kondo Model

Quantum impurity models provide a paradigmatic setting for studying Kondo screening, boundary criticality, and impurity entropy. While these phenomena are well understood in unitary systems, their fate in non-Hermitian many-body settings remains largely unexplored. We study a $\mathscr{PT}$-symmetric quantum impurity model consisting of a unitary SU(2)$_1$ Wess--Zumino--Witten bulk attached to two impurity spins through complex-conjugate Kondo couplings. Using an integrable lattice realization solved by the Bethe Ansatz and benchmarked against finite-temperature matrix-product-state calculations, we determine the impurity free energy, entropy, and the corresponding $g$-function. We identify three distinct impurity phases. In the Kondo-screened phase, the spectrum remains real and the impurity entropy decreases monotonically from $\ln 4$ in the ultraviolet to $0$. Remarkably, this monotonic flow persists despite the nonunitary boundary interaction, beyond the standard domain of the $g$-theorem. The Yu--Shiba--Rusinov phase instead exhibits spontaneous $\mathscr{PT}$-symmetry breaking and loss of boundary conformal invariance, while the local-moment phase displays cyclic renormalization-group flow, with identical impurity entropy and $g$-value in the ultraviolet and infrared limits.

cond-mat.str-el↗

arXiv2026

Breakdown of Monotonic Impurity Entropy Flow in $\mathscr{PT}$-Symmetric Multichannel Kondo Systems

We study a $\mathscr{PT}$-symmetric non-Hermitian multichannel Kondo model consisting of a pair of spin-$\frac12$ impurities coupled to $n$ conduction-electron channels through complex-conjugate Kondo couplings. The impurity renormalization-group (RG) flow is characterized by the Kondo scale $T_K$ and a dimensionless non-Hermiticity parameter $α$. As $α$ increases, the exact Bethe Ansatz solution exhibits four impurity phases: overscreened Kondo, zero mode, Yu--Shiba--Rusinov (YSR), and local moment. The Kondo, zero-mode, and local-moment phases are $\mathscr{PT}$-unbroken, whereas the YSR phase spontaneously breaks $\mathscr{PT}$ symmetry. Using a generalized thermodynamic Bethe Ansatz, we determine the impurity free energy and Affleck--Ludwig $g$-function throughout the $\mathscr{PT}$-unbroken phases. In the Kondo phase, the defect RG flow connects the ultraviolet and infrared conformal fixed points, with the impurity entropy flowing from $2\ln2$ to $2\ln\left[2\cos\left(\fracπ{n+2}\right)\right]$, in agreement with defect conformal field theory. In the zero-mode phase, zero-energy impurity strings reorganize the spectrum into multiple excitation towers, while in the local-moment phase, the RG flow becomes cyclic, returning to the unscreened local-moment fixed point. We conjecture that RG irreversibility, and hence a generalized Affleck--Ludwig $g$-theorem, survives throughout the Kondo phase. Our exact solution nevertheless shows that a real spectrum and defect entropies consistent with defect CFT do not guarantee RG irreversibility: the impurity entropy is non-monotonic in both the zero-mode and local-moment phases.

cond-mat.str-el↗

arXiv2026

Boundary phases and thermodynamics of the Kondo spin-$s$ chain: from overscreened Kondo to boundary-bound states

We study a spin-$\frac12$ impurity coupled to the boundary of a strongly correlated spin-$s$ Takhtajan--Babujian chain, an integrable model whose low-energy physics is described by a perturbed $SU(2)_{2s}$ Wess--Zumino--Witten conformal field theory. While boundary conformal field theory determines the low-energy universality class of the weak-coupling regime, exact Bethe Ansatz methods reveal a sequence of boundary quantum phase transitions in which impurity-bound states emerge and reorganize the Hilbert space into multiple excitation towers built on distinct boundary configurations. This tower restructuring provides the organizing principle for a rich boundary phase diagram extending beyond the conventional Kondo regime. Weak antiferromagnetic coupling realizes the overscreened $2s$-channel Kondo universality class, whereas stronger couplings generate localized boundary modes and qualitatively new screening mechanisms. To describe the resulting thermodynamics, we develop a generalized thermodynamic Bethe Ansatz framework that captures the multi-tower structure across all regimes. The impurity entropy reproduces the boundary conformal field theory prediction in the overscreened Kondo regime but develops pronounced nonmonotonic temperature dependence once boundary-bound states appear, in quantitative agreement with large-scale finite-temperature matrix-product-operator simulations. Complementary dynamical calculations reveal sharp threshold features in the impurity spectral function that directly track the underlying tower structure. Together, boundary conformal field theory, exact Bethe Ansatz, generalized thermodynamic Bethe Ansatz, and tensor-network simulations provide a unified description of impurity screening, boundary-bound-state formation, and excitation-tower reconstruction in a correlated spin-$s$ chain.

cond-mat.str-el↗

arXiv2026

Dissipation driven phase transition in the non-Hermitian Kondo model

Non-Hermitian Hamiltonians capture several aspects of open quantum systems, such as dissipation of energy and non-unitary evolution. An example is an optical lattice where the inelastic scattering between the two orbital mobile atoms in their ground state and the atom in a metastable excited state trapped at a particular site and acting as an impurity, results in the two body losses. It was shown in \cite{nakagawa2018non} that this effect is captured by the non-Hermitian Kondo model. which was shown to exhibit two phases depending on the strength of losses. When the losses are weak, the system exhibits the Kondo phase and when the losses are stronger, the system was shown to exhibit the unscreened phase where the Kondo effect ceases to exist, and the impurity is left unscreened. We re-examined this model using the Bethe Ansatz and found that in addition to the above two phases, the system exhibits a novel $\widetilde{YSR}$ phase which is present between the Kondo and the unscreened phases. The model is characterized by two renormalization group invariants, a generalized Kondo temperature $T_K$ and a parameter `$α$' that measures the strength of the loss. The Kondo phase occurs when the losses are weak which corresponds to $0<α<π/2$. As $α$ approaches $π/2$, the Kondo cloud shrinks resulting in the formation of a single particle bound state which screens the impurity in the ground state between $π/2<α<π$. As $α$ increases, the impurity is unscreened in the ground state but can be screened by the localized bound state for $π<α<3π/2$. When $α>3π/2$, one enters the unscreened phase where the impurity cannot be screened. We argue that in addition to the energetics, the system displays different time scales associated with the losses across $α=π/2$, resulting in a phase transition driven by the dissipation in the system.

cond-mat.str-el↗

arXiv2025

Multichannel Kondo Effect in Superconducting Leads

The traditional multichannel Kondo effect takes place when several gapless metallic electronic channels interact with a localized spin-$S$ impurity, with the number of channels $n$ exceeding the size of the impurity spin, $n>2S$, leading to the emergence of non-Fermi liquid impurity behavior at low temperatures. Here, we show that the effect can be realized even when the electronic degrees of freedom are strongly correlated and gapped. The system under consideration consists of a single spin-$\frac{1}{2}$ impurity coupled isotropically to $n$ spin singlet superconducting channels realized by one-dimensional leads with quasi-long-range superconducting order. The competition between the Kondo and superconducting fluctuations induces multiple distinct ground states and boundary phases depending on the relative strengths of the bulk and boundary interactions. Using the Bethe Ansatz technique, we identify four regimes: an overscreened Kondo phase, a zero-mode phase, a Yu-Shiba-Rusinov (YSR) phase, and a local-moment phase with an unscreened impurity, each with its own experimental characteristic. We describe the renormalization-group flow, the excitation spectrum, and the full impurity thermodynamics in each phase. Remarkably, even in the presence of a bulk mass gap, the boundary critical behavior in the Kondo phase is governed by the same exponents as in the gapless theory with the low-energy impurity sector flowing to the $SU(2)_n$ Wess-Zumino-Witten (WZW) fixed point, and the impurity entropy monotonically decreasing as a function of temperature. In both the overscreened Kondo and zero-mode phases, the residual impurity entropy is $S_{\mathrm{imp}}(T \to 0) = \ln[2\cos(π/(n+2))]$. In the YSR and unscreened phases on the other hand the impurity entropy exhibits non-monotonic temperature dependence and is effectively free at low temperatures with $S_{\mathrm{imp}}(T \to 0) = \ln 2$.

cond-mat.str-el↗

arXiv2025

Competing color superconductivity and color Kondo effect in quark matter

The competition between bulk color superconductivity and the localized screening of a heavy quark impurity, analogous to the Kondo effect, leads to a rich spectrum of phenomena in dense quark matter. We investigate this competition at the edge of a superconducting quark bulk, where both the superconducting gap and the Kondo scale are dynamically generated in a tractable toy model. Utilizing the exact Bethe Ansatz method, we elucidate the resulting boundary physics. We identify distinct regimes characterized by either multi-particle Kondo screening or an unscreened local moment. Crucially, we also uncover a novel intermediate phase featuring impurity screening through a single-particle bound state formed within the superconducting gap. The toy model presented in this work highlights the complex interplay between dynamically generated bulk properties and boundary impurities in extreme QCD environments, offering potential insights into phenomena occurring in heavy-ion collisions and compact stars.

hep-th↗

arXiv2025

Thermodynamics in a split Hilbert space: Quantum impurity at the edge of a one-dimensional superconductor

We present a thermodynamic description of a single magnetic impurity at the edge of a superconducting wire. The impurity exhibits four phases $\unicode{x2014}$ Kondo, Yu-Shiba-Rusinov (YSR) I and II, and local moment $\unicode{x2014}$ a phase diagram richer than in the gapless case, contrary to the expectation that the effects of impurities in gapped hosts are less consequential. We derive the impurity contribution to free energy $F_{\rm imp}(T)$ and entropy in each phase: in Kondo phase, the entropy flows monotonically from $\ln 2$ (UV) to 0 (IR) with critical exponents same as that of the conventional Kondo model; in YSR phases, thermal activation of a midgap bound state produces entropy overshoots above $\ln 2$, saturating to $\ln 2$ at high $T$ and approaching either 0 or $\ln 2$ at low $T$ depending on whether impurity is screened or not; in the local-moment phase the impurity remains effectively decoupled, with entropy near $\ln 2$, with some intermediate-temperature features that progressively fade as $δ\to 0$. These behaviors, including the entropy overshoots in the YSR and local-moment phases, stem from a splitting of the Hilbert space into distinct excitation towers: one in the Kondo phase, two in YSR~I, and three in YSR~II and the local-moment phase. Resolving these tower structures and thereby going beyond conventional TBA yields closed-form analytic expressions for the impurity contribution to the free energy and entropy across the entire phase diagram.

cond-mat.str-el↗

arXiv2025

Thermodynamics in a split Hilbert space: Quantum impurity at the edge of the Heisenberg chain

We study the isotropic spin-$\frac{1}{2}$ Heisenberg chain with a single edge-coupled impurity of arbitrary exchange strength $J$. The model exhibits four impurity phases. For antiferromagnetic couplings ($J>0$): a \textit{Kondo phase} at weak $J$, where the impurity is screened by many-body excitations and the impurity entropy decreases monotonically from $\ln 2$ at $T \to \infty$ to $0$ at $T\to 0$; and an \textit{antiferromagnetic bound-mode (ABM) phase} at strong $J$, where the impurity screened by an exponentially localized bound mode drives $S_{\mathrm{imp}}(T)$ nonmonotonically, with undershoots below zero at intermediate temperatures, while tending to $\ln 2$ as $T \to \infty$ and to $0$ as $T \to 0$. For ferromagnetic couplings ($J<0$): a local-moment (LM) phase at weak $|J|$, where the impurity remains unscreened with $S_{\mathrm{imp}}\to \ln 2$ as $T \to 0$ but exhibits shallow undershoots at intermediate scales; and a \textit{ferromagnetic bound-mode (FBM) phase} at strong $|J|$, where $S_{\mathrm{imp}}=\ln 2$ in both UV and IR limits, yet develops an intermediate-temperature undershoot. We provide an analytic understanding of this behavior, showing that the undershoots originate from the fractionalization of the Hilbert space into several towers of states: for antiferromagnetic couplings this occurs only at strong $J$, driven by boundary-localized bound modes, while for ferromagnetic couplings undershoots occur for all $J<0$, becoming deeper with increasing $|J|$ and vanishing as $J\to 0^{-}$. These bound modes screen the impurity. Incorporating the bound modes and edge states provides a complete analytic understanding of this phenomenon and yields closed expressions for the impurity contribution to free energy and entropy that are valid across all phases. These are checked and found to be in excellent agreement with tensor network and exact diagonalization results.

cond-mat.str-el↗

arXiv2025

Kondo overscreening in the presence of superconductivity

We consider a model describing a system where the superconductivity competes with the overscreened Kondo effect. The model consists of a single spin$-\frac{1}{2}$ quantum impurity at the edge of a quantum wire where spin$-1$ bulk fermions interact attractively, generating a (superconducting) mass gap. The competition between the Kondo screening and the superconductivity leads to a rich phase structure. We find that for strong Kondo coupling, there is a regime of phase space where the Kondo phase is stable with the impurity \textit{overscreened} by a multiparticle Kondo effect, and a Kondo scale is dynamically generated. When the bulk and boundary interaction strength are comparable, we find that a midgap state appears in the spectrum and screens the impurity, while in the ground state, the impurity is unscreened. This midgap state is akin to the Yu-Shiba-Rusinov (YSR) states that exist in the entire phase space in the BCS superconductor. Moreover, when the bulk superconducting interaction strength is stronger than the boundary Kondo interaction strength, the impurity can no longer be screened. Further, between the Kondo and YSR phases, we find a novel phase where, while the Kondo cloud overscreens the impurity, a boundary excitation exists that has vanishing energy in the thermodynamic limit. Similar phase diagrams that result from competition between different mechanisms were found for other models, too: the dissipative Kondo system, where dissipation competes with screening; the Kondo impurity coupled to spin-1/2 attractively interacting fermions where condensation competes with screening; and the XXX-Kondo model, where the lattice cutoff and the bulk spin interaction compete with screening.

cond-mat.str-el↗

arXiv2020

AGT basis in SCFT for c=3/2 and Uglov Polynomials

AGT allows one to compute conformal blocks of d = 2 CFT for a large class of chiral CFT algebras. This is related to the existence of a certain orthogonal basis in the module of the (extended) chiral algebra. The elements of the basis are eigenvectors of a certain integrable model, labeled in general by N-tuples of Young diagrams. In particular, it was found that in the Virasoro case these vectors are expressed in terms of Jack polynomials, labeled by 2-tuples of ordinary Young diagrams, and for the super-Virasoro case they are related to Uglov polynomials, labeled by two colored Young diagrams. In the case of a generic central charge this statement was checked in the case when one of the Young diagrams is empty. In this note we study the N=1 SCFT and construct 4 point correlation function using the basis. To this end we need to clarify the connection between basis elements and Uglov polynomials, we also need to use two bosonizations and their connection to the reflection operator. For the central charge $c=3/2$ we checked that there is a connection with the Uglov polynomials for the whole set of diagrams.

hep-th↗