arXiv subjects

Parameshwar R. Pasnoori

Publications and source records attributed to Parameshwar R. Pasnoori.

At least 19 recordsLinked to original sources

arXiv2026

RG Limit Cycles in BKT Flows $\equiv$ Periodic Real-Time Dynamics in the Current-Current Perturbed $SU(2)_1$ WZW Model

We establish an exact correspondence between renormalization-group (RG) evolution and real-time quantum dynamics in the anisotropic current-current perturbed $SU(2)_1$ Wess-Zumino-Witten (WZW) model. Using its integrable fermionic representation, we construct the exact time-dependent many-body wavefunction by means of the generalized Bethe ansatz and show that periodic boundary conditions lead to quantum Knizhnik-Zamolodchikov equations associated with the XXZ trigonometric $R$-matrix, which corresponds to the quantum affine algebra $\mathcal{U}_q(\widehat{\mathfrak{sl}_2})$ evaluated in its spin-$1/2$ evaluation representation. Consistency of these equations constrains the temporal evolution of the longitudinal and transverse interaction strengths. In the universal regime, these integrability conditions are exactly equivalent to the Berezinskii-Kosterlitz-Thouless RG flow equations upon identifying physical time with the logarithmic RG scale. Consequently, the RG limit cycles of the anisotropic current-current perturbed $SU(2)_1$ WZW model are realized as periodic real-time evolution of its interaction strengths. Our results provide an exact dynamical realization of RG limit cycles and establish a direct connection between cyclic RG flows, quantum integrability, and periodically driven interacting quantum field theories.

hep-th↗

arXiv2026

Exact many-body wavefunction of the Kondo model with time-dependent interaction strength

Quantum integrability has been applied to a large variety of low dimensional Hamiltonians in Quantum Field Theory, Condensed Matter Physics, and Statistical Mechanics to obtain exact expressions for the spectrum and thermodynamics of these systems. In most of these studies the coupling constants are constant in time. Here we present an exact solution of the nonstationary Schrödinger equation for the Kondo Hamiltonian with a time-dependent spin-exchange coupling $J(t)$ of the form $λt + p(t) \pm \sqrt{(λt + p(t))^2 + 16/3}$, where $p(t)$ is an arbitrary periodic function, under periodic boundary conditions. Unlike previously studied time-dependent integrable models, which are rooted in the classical Yang--Baxter structure and associated Knizhnik--Zamolodchikov equations, our approach is based on the quantum Knizhnik--Zamolodchikov framework and the quantum Yang--Baxter algebra. Our results broaden the domain of time-dependent integrability to a genuinely quantum class of models and provide a new tools for exploring coherent nonequilibrium dynamics in strongly correlated systems.

cond-mat.str-el↗

arXiv2026

Boundary Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-Dependent Bulk and Boundary Coupling Strengths

The generalized Bethe ansatz framework formulated in [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)] provides a unified framework to find exact solutions to quantum many-body systems with time-dependent coupling strengths with periodic boundary conditions. In this work we extend this framework to the case of open boundary conditions where in addition to the time-dependent interactions in the bulk, the boundary conditions are explicitly time-dependent. We show that for integrable time-dependent bulk coupling strengths, the generalized Bethe ansatz framework provides the time-dependent boundary conditions compatible with integrability and reduces the time-dependent Schrodinger equation to a set of matrix difference equations called the boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations. The solution to the BqKZ equations provides the explicit form of the exact wavefunction. We further show that the RG invariants of the corresponding static model identify with the dynamical invariants in the time-dependent model.

math-ph↗

arXiv2026

Beyond Integrability Preserving Renormalization-Group Protocol in Non-Hermitian Hamiltonians with Time-Dependent Interaction Strengths

It is well established that in time-dependent quantum systems, integrability preserving time-dependent interaction strengths are identical to the renormalization group (RG) trajectories of the corresponding static model when time `$t$' in the driven model is identified with the logarithm of the cutoff `$\logΛ$' of the static model. We refer to this integrability preserving driving as the RG protocol. In this work we extend the class of time-dependent integrable models to include non-Hermitian quantum models with time-dependent interaction strengths. Using the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that the constraints imposed by integrability are more general: The interaction strengths of the static model that flow in the RG follow the respective RG trajectories in the corresponding time-dependent model as described above. In addition, the interaction strengths of the static model that are RG invariant can either be constant or have a specific time-dependence in the corresponding time-dependent model which is constrained by integrability. Thus we establish that in the context of time-dependent non-Hermitian systems, the set of integrability preserving time-dependent strengths is larger than the set corresponding to the RG protocol.

quant-ph↗

arXiv2026

Quantum Knizhnik-Zamolodchikov Equations and Integrability of Quantum Field Theories with Time-dependent Interaction Strength

In this paper we consider the problem of solving quantum field theories with time dependent interaction strengths. We show that the recently formulated framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], which is a generalization of the regular Bethe ansatz technique, provides the exact many-body wavefunction. In this framework, the time-dependent Schrodinger equation is reduced to a set of analytic difference equations and matrix difference equations, called the quantum Knizhnik-Zamolodchikov (qKZ) equations. The consistency of the solution gives rise to constraints on the time-dependent interaction strengths. For interaction strengths satisfying these constraints, the system is integrable, and the solution to the qKZ and the analytic difference equations provides the explicit form of the many-body wavefunction that satisfies the time-dependent Schrodinger equation. We provide a concrete example by considering the $SU(2)$ Gross-Neveu model with time dependent interaction strength. Using this framework we solve the model with the most general time-dependent interaction strength and obtain the explicit form of the wave function.

math-ph↗

arXiv2026

Quantum Integrability of Hamiltonians with Time-Dependent Interaction Strengths and the Renormalization Group Flow

In this paper we consider quantum Hamiltonians with time-dependent interaction strengths, and following the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that constraints imposed by integrability take the same form as the renormalization group flow equations corresponding to the respective Hamiltonians with constant interaction strengths. As a concrete example, we consider the anisotropic time-dependent Kondo model characterized by the time-dependent interaction strengths $J_{\parallel}(t)$ and $J_{\perp}(t)$. We construct an exact solution to the time-dependent Schrodinger equation and by applying appropriate boundary conditions on the fermion fields we obtain a set of matrix difference equations called the quantum Knizhnik-Zamolodchikov (qKZ) equations corresponding to the XXZ R-matrix. The consistency of these equations imposes constraints on the time-dependent interaction strengths $J_{\parallel}(t)$ and $J_{\perp}(t)$, such that the system is integrable. Remarkably, the resulting temporal trajectories of the couplings are shown to coincide exactly with the RG flow trajectories of the static Kondo model, establishing a direct and universal correspondence between integrability and renormalization-group flow in time-dependent quantum systems.

quant-ph↗

arXiv2026

Time-Dependent Dynamical Dimensional Transmutation in the $SU(2)$ Gross-Neveu Model with Time-Dependent Interaction Strength

In this work we study driven $SU(2)$ Gross-Neveu (GN) model whose time-dependent interaction strength is constrained by quantum integrability within the recently developed generalized Bethe ansatz framework. Integrability requires the coupling strengths to evolve according to the same equation as the renormalization-group (RG) flow of the corresponding static theory, where time `$t$' of the time-dependent model is identified with the logarithm of the cutoff `$\ln Λ$' of the static model. We reformulate the exact quantum Knizhnik-Zamolodchikov (qKZ) solution in terms of a Yang-Yang functional, whose saddle-point equations determine the long-time dynamics of the system. In the scaling regime, this analysis reveals the emergence of a characteristic time scale $t_0$. In the case of coupling strength decreasing with time, we show that in the adiabatic regime, which corresponds to $t\sim t_0$ for drive rate $α_0=1$, the system exhibits a dynamically generated time-dependent mass gap, which at time $t=t_0+Δt$ is given by $m(t)=m_0 e^{-πα_0Δt}$, where $m_0=Λe^{-πα_0 t_0}$, which possesses the same functional dependence as the non-perturbatively generated mass scale of the static GN model. We thereby establish a time-dependent analogue of dynamical dimensional transmutation and identify the adiabatic regime of the driven system with the scaling regime of the static theory. In the case of very large time scales $t\gg t_0$ for drive rate $α_0$ or for very fast drive rates $α$ such that $αt \gg α_0t_0$, for any $t<L$, we argue that the system is asymptotically free and approaches the $SU(2)_1$ WZNW model, which corresponds to the UV fixed point of the $SU(2)$ GN model.

math-ph↗

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

Integrability of the Kondo model with time dependent interaction strength

In this letter we consider the time dependent Kondo model where a magnetic impurity interacts with the electrons through a time dependent interaction strength $J(t)$. We develop a new framework based on Bethe ansatz and construct an exact solution to the time-dependent Schrodinger equation. We show that when periodic boundary conditions are applied, the consistency of the solution results in a constraint equation which relates the amplitudes corresponding to a certain ordering of the particles in the configuration space. This constraint equation takes the form of a matrix difference equation, and the associated consistency conditions restrict the interaction strength $J(t)$ for the system to be integrable. For a given $J(t)$ satisfying these constraints, the solution to the matrix difference equations provides the exact many-body wavefunction that satisfies the time-dependent Schrodinger equation. We provide a concrete example of $J(t)$ which satisfies these constraint equations. We show that in this case, the matrix difference equations turn into quantum Knizhnik-Zamolodchikov (qKZ) equations, which are well studied in the literature. The framework developed in this work allows one to probe the non-equilibrium physics of the Kondo model, and being general, it also allows one to solve new class of Hamiltonians with time-dependent interaction strength which are based on quantum Yang-Baxter algebra.

cond-mat.str-el↗

arXiv2025

Exact solution of a non-Hermitian $\mathscr{PT}$-symmetric Heisenberg spin chain

We construct the exact solution of a non-Hermitian $\mathscr{PT}$-symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases we refer to as $A$ and $B$ phases. In the $B$ type phase, the $\mathscr{PT}$- symmetry remains unbroken and it consists of eigenstates with only real energies, whereas the $A$ type phase contains a $\mathscr{PT}$-symmetry broken sector comprised of eigenstates with only complex energies and a sector of unbroken $\mathscr{PT}$-symmetry with eigenstates of real energies. The $\mathscr{PT}$-symmetry broken sector consists of pairs of eigenstates whose energies are complex conjugates of each other. The existence of two sectors in the $A$ type phase is associated with the exponentially localized bound states at the edges with complex energies which are described by boundary strings. We find that both $A$ and $B$ type phases can be further divided into sub-phases which exhibit different ground states. We also compute the bound state wavefunction in one magnon sector and find that as the imaginary value of the boundary parameter is increased, the exponentially localized wavefunction broadens thereby protruding more into the bulk, which indicates that exponentially localized bound states may not be stabilized for large imaginary values of the boundary parameter.

quant-ph↗

arXiv2025

Complete Boundary Phase Diagram of the Spin-$\frac{1}{2}$ XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime

We consider the spin $\frac{1}{2}$ XXZ chain with diagonal boundary fields and solve it exactly using Bethe ansatz in the gapped anti-ferromagnetic regime and obtain the complete phase boundary diagram. Depending on the values of the boundary fields, the system exhibits several phases which can be categorized based on the ground state exhibited by the system and also based on the number of bound states localized at the boundaries. We show that the Hilbert space is comprised of a certain number of towers whose number depends on the number of boundary bound states exhibited by the system. The system undergoes boundary phase transitions when boundary fields are varied across certain critical values. There exist two types of phase transitions. In the first type the ground state of the system undergoes a change. In the second type, named the `Eigenstate phase transition', the number of towers of the Hilbert space changes, which is again associated with the change in the number of boundary bound states exhibited by the system. We use the DMRG and exact diagonalization techniques to probe the signature of the Eigenstate phase transition and the ground state phase transition by analyzing the spin profiles in each eigenstate.

cond-mat.str-el↗

arXiv2025

Interplay between Symmetry Breaking and Interactions in a Symmetry Protected Topological Phase

We solve the one dimensional massive Thirring model or equivalently the sine-Gordon model in the repulsive regime with general Dirichlet boundary conditions, which are characterized by two boundary fields $ϕ_{L,R}$ associated with the left and right boundaries respectively. In the presence of these boundary fields, which explicitly break the charge conjugation symmetry, the system exhibits a duality symmetry which changes the sign of the mass parameter $m_0$ and shifts the values of the boundary fields by $ϕ_{L,R}\rightarrow ϕ_{L,R}+π$. When the mass parameter $m_0<0$ and the boundary fields $ϕ_{L,R}=0$, or equivalently due to duality symmetry, when the mass parameter $m_0>0$ and the boundary fields $ϕ_{L,R}=π$, the system is at a trivial point. Here, the ground state is unique just as in the case of periodic boundary conditions. In contrast, when the mass parameter $m_0<0$ and the boundary fields $ϕ_{L,R}=π$, and equivalently due to the duality symmetry, when the mass parameter $m_0>0$ and the boundary fields $ϕ_{L,R}=0$, the system is at a topological point where it exhibits a symmetry protected topological (SPT) phase, which is characterized by the existence of zero energy bound states at both the boundaries. For a given value of the mass parameter $m_0$, we find that these phases remain stable in the presence of symmetry breaking fields at the boundary, provided they are smaller than certain critical values which depend on the strength of the interactions in the bulk. Hence, we show that the stability of the SPT and trivial phases depends on the interplay of the symmetry breaking boundary field values and the bulk interaction strength.

hep-th↗

arXiv2025

Emergent boundary supersymmetry in a one dimensional superconductor

The interplay between bulk properties and boundary conditions in one-dimensional quantum systems, gives rise to many intriguing phenomena. These include the emergence of zero energy modes which are of significant interest to a variety of fields. In this work we investigate the presence of such zero modes in cases where the boundary conditions are dynamical and arise due to the coupling to some quantum degrees of freedom. In particular, we study a one-dimensional spin-singlet superconductor, modeled by the Gross-Neveu field theory, coupled to spin $\frac{1}{2}$ magnetic impurities at its boundaries via a spin-exchange interaction. We solve the model exactly for arbitrary values of the bulk and the impurity coupling strengths using nested coordinate Bethe ansatz and show that the system exhibits a rich boundary phase structure. For a range of couplings, the low energy degrees of freedom form irreducible representations of the supersymmetric $spl(2,1)\otimes spl(2,1)$ algebra which become degenerate at a specific point, indicating the emergence of supersymmetry in the low energy boundary degrees of freedom. We show that at the supersymmetric point there exist exact zero energy modes that map one ground state with the other. We express these in terms of the generators of the algebra.

cond-mat.str-el↗

arXiv2025

Edge modes and boundary impurities in the anisotropic Heisenberg spin chain

We present a comprehensive analysis of boundary phenomena in a spin-$\frac{1}{2}$ anisotropic Heisenberg chain (XXZ-$\frac{1}{2}$) in the gapped antiferromagnetic phase, with a particular focus on the interplay between fractionalized spin-$\frac{1}{4} $ edge modes and a coupled spin-$\frac{1}{2}$ impurity at the edge. Employing a combination of Bethe Ansatz, exact diagonalization, and density matrix renormalization group (DMRG) methods, we explore the intricate phase diagram that emerges when the impurity is coupled either integrably or non-integrably to the chain. For integrable antiferromagnetic impurity couplings, we identify two distinct phases: the Kondo phase, where the impurity is screened by a multiparticle Kondo effect, and the antiferromagnetic bound mode phase, where an exponentially localized bound state screens the impurity in the ground state. When coupled ferromagnetically while maintaining integrability, the impurity behaves as a free spin-$\frac{1}{2}$, leading to either a ferromagnetic bound mode phase, where the impurity remains free in the ground state but may be screened at higher energy excitations or an unscreened (or local moment) phase where impurity remains unscreened in every eigenstate whereas for non-integrable ferromagnetic coupling, the impurity is not free. In the case of non-integrable antiferromagnetic coupling, a third phase emerges, characterized by mid-gap excitations with two degenerate states below the mass gap on top of the Kondo and antiferromagnetic bound mode phases, further enriching the phase diagram. Our findings highlight the nuanced behavior of boundary impurities in gapped antiferromagnetic systems, offering new insights into Kondo effects and impurity screening in the presence of fractionalized edge modes and bulk antiferromagnetic order.

cond-mat.str-el↗

arXiv2025

Duality symmetry, zero energy modes and boundary spectrum of the sine-Gordon/massive Thirring model

We solve the one-dimensional massive Thirring model, which is equivalent to the one-dimensional sine-Gordon model, with two types of Dirchlet boundary conditions: open boundary conditions (OBC) and twisted open boundary conditions ($\widehat{\text{OBC}}$). The system exhibits a duality symmetry which relates models with opposite bare mass parameters and boundary conditions, i.e: $m_0 \leftrightarrow - m_0$, $\text{OBC}\leftrightarrow\widehat{\text{OBC}}$. For $m_0<0$ and OBC, the system is in a trivial phase whose ground state is unique, as in the case of periodic boundary conditions. In contrast, for $m_0<0$ and $\widehat{\text{OBC}}$, the system is in a topological phase characterized by the existence of zero energy modes (ZEMs) localized at each boundary. As dictated by the duality symmetry, for $m_0>0$ and $\widehat{\text{OBC}}$, the trivial phase occurs, whereas the topological phase occurs for $m_0>0$ and OBC. In addition, we analyze the structure of the boundary excitations, finding significant differences between the attractive $(g>0)$ and the repulsive $(g<0)$ regimes.

hep-th↗

arXiv2025

Realizing a Symmetry Protected Topological Phase in a Superconducting Circuit

We propose a superconducting quantum circuit whose low-energy degrees of freedom are described by the sine-Gordon (SG) quantum field theory. For suitably chosen parameters, the circuit hosts a symmetry protected topological (SPT) phase protected by a discrete $\mathbb{Z}_2$ symmetry. The ground state of the system is twofold degenerate and exhibits local spontaneous symmetry breaking of the $\mathbb{Z}_2$ symmetry close to the edges of the circuit, leading to spontaneous localized edge supercurrents. The ground states host Majorana zero modes (MZM) at the edges of the circuit. On top of each of the two ground states, the system exhibits localized bound states at both edges, which are topologically protected against small disorder in the bulk. The spectrum of these boundary excitations should be observable in a circuit-QED experiment with feasible parameter choices.

quant-ph↗

arXiv2024

A spin chain with non-Hermitian $\mathscr{PT}-$symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge

We construct an exactly solvable $\mathscr{PT}-$symmetric non-Hermitian model where a spin$-\frac{1}{2}$ isotropic quantum Heisenberg spin chain is coupled to two spin$-\frac{1}{2}$ Kondo impurities at its boundaries with coupling strengths that are complex conjugates of each other. Solving the model by means of a combination of the Bethe Ansatz and density matrix renormalization group (DMRG) techniques, we show that the model exhibits three distinct boundary phases: a $\mathscr{PT}$ symmetric phase with a dissipative Kondo effect, a phase with bound modes and spontaneously broken $\mathscr{PT}$ symmetry, and a phase with an effectively unscreened spin (i.e. a free local moment). In the Kondo and the unscreened phases, the $\mathscr{PT}-$symmetry is unbroken, and hence all states have real energies, whereas in the bound mode phases, in addition to the states with real energies, there exist states with complex energy eigenvalues that appear in complex conjugate pairs, signaling spontaneous breaking of the $\mathscr{PT}-$symmetry. The exact solution is used to provide an accessible benchmark for DMRG with a non-Hermitian matrix product operator representation that demonstrates an accuracy comparable to its Hermitian limit thus showing the power of DMRG to handle non-Hermitian many body calculations.

cond-mat.str-el↗

arXiv2023

Spin fractionalization and zero modes in the spin-$\frac{1}{2}$ XXZ chain with boundary fields

In this work we argue that the antiferromagnetic spin $\frac{1}{2}$ XXZ chain in the gapped phase with boundary magnetic fields hosts fractional spin $\frac{1}{4}$ at its edges. Using a combination of Bethe ansatz and the density matrix renormalization group we show that these fractional spins are sharp quantum observables in both the ground and the first excited state as the associated fractional spin operators have zero variance. In the limit of zero edge fields, we argue that these fractional spin operators once projected onto the low energy subspace spanned by the ground state and the first excited state, identify with the strong zero energy mode discovered by P. Fendley \cite{Fendley}.

cond-mat.str-el↗