arXiv subjects

Andreas Gleis

Publications and source records attributed to Andreas Gleis.

16 recordsLinked to original sources

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.

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arXiv2026

Interplay of spin-orbit coupling, crystal field splitting and correlations: a ghost rotationally invariant slave boson treatment

We investigate the interplay of spin-orbit coupling, crystal field splittings, and electronic correlations in the $t_{2g}$ Hubbard-Kanamori model within the recently formulated ghost rotationally invariant slave-boson method (GRISB). In particular, we study a tight binding model of Sr$_2$RuO$_4$ with parameters extracted from density functional theory and linearized quasiparticle self-consistent GW (LQSGW) calculations; we study the behavior of different physical quantities as the number of ghosts increases to examine the convergence of GRISB to dynamical mean field theory (DMFT) and experimental results; and we leverage the ability of GRISB to investigate the model over a wide range of parameters at low temperature. In particular, we examine both static and dynamical observables driven by the spin orbit coupling (SOC) and study how they vary as a function of the Hubbard $U$ and Hund's coupling $J$. GRISB converges quickly for most of these observables, and the calculations reveal the following: $U$ enhances the spin-orbit coupling while $J$ suppresses it. We also study the shape of the Fermi surface within different methodologies, and examine the Lifshitz transition which takes place as a function of strain in this material.

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arXiv2026

Quantum criticality in the two-dimensional Hubbard model

We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, $U=7t$ and $t'=-0.3t$, we find a critical doping $p^{\ast}$ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and $d_{x^2-y^2}$-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at $p^{\ast}$. As $p^{\ast}$ is crossed from the normal Fermi liquid at $p>p^{\ast}$ into the pseudogap metal at $p<p^{\ast}$, the coherent low-energy spectral weight in the antinodal region is lost and replaced by a narrow, metallic pseudogap, while the nodal region evolves smoothly and remains comparatively coherent. This gives rise to Fermi arcs in the pseudogap metal at $p<p^{\ast}$, since the zero-frequency spectral weight remains large in the nodal region but is strongly suppressed in the antinodal region.

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arXiv2026

Dynamical scaling near the pseudogap quantum critical point of the two-dimensional Hubbard model

We study dynamical scaling in the quantum-critical fan of the pseudogap-metal to Fermi-liquid transition of the two-dimensional Hubbard model. Using a four-patch dynamical cluster approximation with the numerical renormalization group as a cluster impurity solver, we access real-frequency dynamics over several decades at arbitrary temperatures. Close to the critical doping, the local spin and cluster-current susceptibility spectra exhibit $x=\omega/T$ scaling of the form $\chi''(\omega,T)\sim \tanh(x/2)$, and the cluster contribution to the optical conductivity obeys $T\sigma'_{\mathrm{cl}}(\omega,T) \sim \tanh(x/2)/x$, implying a $1/T$ cluster dc conductivity. In the scaling regime, the vertex contribution to the cluster optical response is much larger than the bubble contribution. We further find evidence for a marginal-Fermi-liquid nodal self-energy. This, together with the $1/T$ vertex contribution to the conductivity, implies strange-metal optical transport in the quantum critical region. Our results describe several qualitative aspects of several experimental observations.

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arXiv2026

Symmetric estimator for discrete self-energy of discrete many-body systems

We derive a discrete spectral representation of the single-particle self-energy using a discrete evaluation of Kugler's symmetric improved estimator. Our construction can be used on both the real and the complex (Matsubara) frequency axis. It is guaranteed to remain causal at the numerical level, in contrast to standard approaches that may generate unphysical negative spectral weight or require additional broadening. Our representation can be used for any Hamiltonian; here we apply it to quantum impurity models and in dynamical mean-field theory. The latter is formulated with a discrete hybridization function throughout its self-consistency loop. In both cases and across various numerical methods, we obtain significantly improved accuracy for a range of impurity properties.

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arXiv2026

Topological Kondo Insulator from Spin Loop Currents

We demonstrate that interacting electrons in AB-stacked $\mathrm{MoTe}_2/\mathrm{WSe}_2$ realize a topological Kondo insulator at hole filling $\nu=2$ per moir\'e unit cell. In the presence of only local correlations, a symmetry of the moir\'e-scale bandstructure enforces a compensated topological semimetal by tying band inversion to band overlap. We show that non-local interactions change the physics qualitatively, since they allow intrinsic, quantum-geometry-induced spin loop currents to feed back on the effective bandstructure, which lift the remaining accidental degeneracies and open a full gap in the spectrum, leading to a fully gapped topological Kondo insulator. We establish this using real-frequency dynamical mean-field theory to capture Kondo physics alongside Hartree-Fock for non-local interactions. The topological Kondo insulator emerges at intermediate displacement fields, where strong correlations manifest through an enhanced spin susceptibility, a suppressed charge susceptibility, and a stronger thermal dependence of the resistivity. Our results are in good agreement with recent experiments on $\mathrm{MoTe}_2/\mathrm{WSe}_2$ bilayers demonstrating topological to trivial phase transitions controlled by the displacement field.

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arXiv2026

Pseudogapped Fermi liquids from emergent quasiparticles

We propose an interacting model that is exactly solvable in any spatial dimension and gives rise to a Fermi liquid (FL) featuring a pseudogapped (PG) single-particle spectral function and a vanishing quasiparticle (QP) weight at half-filling, without invoking Mott physics. The PG originates from a purely fermionic mechanism through emergent QPs arising from a correlated hopping interaction. By employing an appropriate coherent-state basis, we derive a Gaussian path-integral representation of the partition function, which enables systematic treatments of deviations from the Gaussian limit using standard many-body techniques, such as diagrammatic perturbation theory or mean-field theory. We explicitly demonstrate and discuss several properties of the exactly solvable limit on the square lattice, including the mechanism for temperature-dependent PG opening, the singular behavior of the self-energy, the violation of the Luttinger sum rule, and the role of Luttinger and Fermi surfaces. Finally, we explore quantum phase transitions between PG-FLs and Landau FLs.

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arXiv2026

Liouvillian interpolation of the self-energy of cluster dynamical mean-field theories

Two widely-used non-local extensions of dynamical mean field theory (DMFT), cellular DMFT (CDMFT) and the dynamical cluster approximation (DCA), both yield self-energies marred by having some unphysical properties: CDMFT yields real-space self-energies that are not translationally invariant, and DCA yields momentum-space self-energies with discontinuities in their momentum dependence. It is often desirable to remove these flaws by post-processing cluster DMFT results, using strategies called periodization for CDMFT and interpolation for DCA -- for brevity, we refer to both cases as interpolation. However, traditional interpolation approaches struggle to capture intricate structures such as hole pockets in the hole-doped square-lattice Hubbard model, as highlighted in Phys. Rev. B 105, 35117 (2022). Further, these approaches interpolate frequency-dependent functions, which may lead to causality violations. Here, we propose Liouvillian interpolation, a novel, intuitive, and robust scheme for interpolating cluster DMFT results. Our key idea is to interpolate frequency-independent matrix elements of the single-particle irreducible part of the Liouvillian, obtained from a continued-fraction expansion of the cDMFT self-energy. We demonstrate that the ingredients of such an expansion possess a more local Fourier expansion than the functions involved in traditional interpolation schemes, and that Liouvillian interpolation inherently conserves causality. We illustrate our method for the one-dimensional Hubbard model using CDMFT, and for the two-dimensional Hubbard model using four-patch DCA. For the latter, we find that L-interpolation can (depending on doping) yield Fermi and Luttinger arcs which together form a closed surface.

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arXiv2025

Tangent space Krylov computation of real-frequency spectral functions: Influence of density-assisted hopping on 2D Mott physics

We present a tangent-space Krylov (TaSK) method for efficient computation of zero-temperature real-frequency spectral functions on top of ground state (GS) matrix product states (MPS) obtained from the Density Matrix Renormalization Group. It relies on projecting resolvents to the tangent space of the GS-MPS, where they can be efficiently represented using Krylov space techniques. This allows for a direct computation of spectral weights and their corresponding positions on the real-frequency axis. We demonstrate the accuracy and efficiency of the TaSK approach by showcasing spectral data for various models. These include the 1D Haldane-Shastry and Heisenberg models as benchmarks. As an interesting application, we study the Hubbard model on a cylinder at half-filling, augmented by a density-assisted hopping (DAH) term. We find that DAH leads to particle-hole asymmetric single-particle mobilities and lifetimes in the resulting Mott insulator, and identify the responsible scattering processes. Further, we find that DAH influences the dispersion of Green's function zeros beyond its range, which has a frustrating effect on the Mott insulator studied here.

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arXiv2025

Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems

We examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency $\omega_0 \ll U/2$, the onsite Coulomb scale $U/2$), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a novel frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling $\alpha^*$ when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast ($\omega_0 \gtrsim U/2$), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively $U_{\text{eff}}$ due to phonon mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group (NRG) calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

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arXiv2025

Reply to comment on "Controlled bond expansion for Density Matrix Renormalization Group ground state search at single-site costs"

We reply to McCulloch and Osborne's recent comment on our manuscript (Phys. Rev. Lett. 130, 246402 (2023)) on controlled bond expansion (CBE) for density matrix renormalization group (DMRG) ground state search. We appreciate their suggestion to consider randomized SVD and address their constructive critique on the variational properties of CBE-DMRG. However, we strongly disagree with their proposal to omit the projection to the 2-site tangent space and explain its importance for efficient bond expansion. In particular, in the context of CBE applied to the time-dependent variational principle (TDVP), we show that omitting this projection can lead to avoidable errors. Lastly, we emphasize the complementary roles of 3S mixing and CBE, reiterating our recommendation from Phys. Rev. Lett. 130, 246402 (2023) to combine both methods (CBE+$\alpha$). We provide examples to demonstrate the superior efficiency and robustness of CBE+$\alpha$.

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arXiv2024

Dynamical scaling and Planckian dissipation due to heavy-fermion quantum criticality

We study dynamical scaling associated with a Kondo-breakdown quantum critical point (KB-QCP) of the periodic Anderson model, treated by two-site cellular dynamical mean-field theory (2CDMFT). In the quantum critical region, the staggered spin exhibits SYK-like slow dynamics and its dynamical susceptibility shows $\omega/T$ scaling. We propose a scaling Ansatz that describes this behavior. It also implies Planckian dissipation for the longest-lived excitations. The current susceptibility follows the same scaling ansatz, leading to strange-metal scaling. This demonstrates that the KB-QCP described by 2CDMFT is an intrinsic (i.e., disorder-free) strange-metal fixed point. Surprisingly, the SYK-like dynamics and scaling are driven by strong vertex contributions to the susceptibilities. Our results for the optical conductivity match experimental observations on YbRh${}_2$Si${}_2$ and CeCoIn${}_5$.

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arXiv2023

Emergent Properties of the Periodic Anderson Model: a High-Resolution, Real-Frequency Study of Heavy-Fermion Quantum Criticality

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory, with the numerical renormalization group (NRG) as an impurity solver. The PAM describes an itinerant $c$ band hybridizing with a localized $f$ band. At $T=0$, it exhibits a hybridization tuned Kondo breakdown quantum critical point (KB-QCP) from a Kondo to an RKKY phase. At the KB-QCP, the $f$ band changes character from itinerant to mainly localized, while the $c$ band remains itinerant. We elucidate its nature in detail by performing a high-resolution, real-frequency study of dynamical quantities. NRG allows us to study the quantum critical non-Fermi-liquid (NFL) regime located between $T_{FL}<T_{NFL}$. Surprisingly, self-consistency is essential to stabilize the NFL and the QCP. The Fermi-liquid (FL) scale $T_{FL}$ decreases towards and vanishes at the QCP. At $T=0$, we find the following properties. The $f$ quasiparticle (QP) weight $Z_f$ decreases continuously as the QCP is approached from either side, vanishing only at the QCP. Therefore, $Z_f$ is nonzero in both the Kondo and the RKKY phase; hence, the FL QP comprise $c$ and $f$ electrons in both phases. The Fermi surface (FS) volumes in the two phases differ. Whereas the large-FS Kondo phase has a usual two-band structure, the small-FS RKKY phase has an unexpected three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and the RKKY phase. The FS reconstruction is accompanied by the appearance of a Luttinger surface (LS) on which the $f$ self-energy diverges. The FS and LS volumes are related to the density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent LS as evidence for $f$-electron fractionalization in the RKKY phase. Our Hall coefficient and specific heat are in good qualitative agreement with experiment.

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arXiv2022

Time-dependent variational principle with controlled bond expansion for matrix product states

We present a controlled bond expansion (CBE) approach to simulate quantum dynamics based on the time-dependent variational principle (TDVP) for matrix product states. Our method alleviates the numerical difficulties of the standard, fixed-rank one-site TDVP integrator by increasing bond dimensions on the fly to reduce the projection error. This is achieved in an economical, local fashion, requiring only minor modifications of standard one-site TDVP implementations. We illustrate the performance of CBE--TDVP with several numerical examples on finite quantum lattices.

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arXiv2022

Controlled bond expansion for DMRG ground state search at single-site costs

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state $\Psi$ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in $H\Psi$ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.

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arXiv2022

Projector formalism for kept and discarded spaces of matrix product states

Any matrix product state $|\Psi\rangle$ has a set of associated kept and discarded spaces, needed for the description of $|\Psi\rangle$, and changes thereof, respectively. These induce a partition of the full Hilbert space of the system into mutually orthogonal spaces of irreducible $n$-site variations of $|\Psi\rangle$. Here, we introduce a convenient projector formalism and diagrammatic notation to characterize these $n$-site spaces explicitly. This greatly facilitates the formulation of MPS algorithms that explicitly or implicitly employ discarded spaces. As an illustration, we derive an explicit expression for the $n$-site energy variance and evaluate it numerically for a model with long-range hopping. We also describe an efficient algorithm for computing low-lying $n$-site excitations above a finite MPS ground state.

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