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Seung-Sup B. Lee

Publications and source records attributed to Seung-Sup B. Lee.

At least 19 recordsLinked to original sources
arXiv2026

Constant-Per-Layer-Depth MPS-Pretrained Ansatz for Noisy Distributed Quantum Processors

Distributed quantum processors could scale variational algorithms beyond single devices, but circuit depth, communication overhead, and noise limit their performance. We compare ladder, mixed-canonical, and brick-wall realizations of matrix-product-state (MPS) pretraining with matched per-layer two-qubit-block resources. Despite comparable ideal variational quantum eigensolver performance and gradient scales, the shallower brick-wall architecture reduces circuit duration, idle-time decoherence, and zero-noise-extrapolation (ZNE) overhead, yielding superior noisy and ZNE-assisted performance. We then extend MPS-pretrained circuits to modular processors with one communication qubit per quantum processing unit (QPU); a nearest-neighbor QPU-path schedule keeps the per-layer depth constant as QPUs are added. Distributed circuits whose inter-QPU links realize long-range interactions of the target Hamiltonian match or outperform the single-processor brick-wall under noise when communication idle time is short compared with the coherence time. These results establish hardware-aware co-design of tensor-network pretraining, circuit scheduling, and communication topology as a principle for variational quantum computation on noisy modular hardware.

quant-ph↗
arXiv2026

Coherent-disorder-driven complexity transitions in a quantum-advantage architecture

While decoherence is known to erode classical hardness in quantum random sampling, the impact of coherent spatial disorder remains an open question. We study a square-lattice instantaneous quantum polynomial-time (IQP) architecture subject to two-qubit gate-angle disorder and single-qubit dephasing using exact tensor-network simulations up to 576 qubits. For finite systems without dephasing, increasing disorder drives two consecutive crossovers toward classical simulability: the output distribution first loses anticoncentration, and then the tensor-network simulation cost drops from exponential to polynomial as entanglement is suppressed. The finite-size scaling collapses are consistent with continuous transitions in the large-system limit. Dephasing further reduces the complexity. We characterize the computationally hard regime through scaling laws that provide quantitative error-budget bounds for realistic near-term devices.

quant-ph↗
arXiv2026

The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap

We present the finite-difference parquet method that greatly improves the applicability and accuracy of two-particle correlation approaches to interacting electron systems. This method incorporates the nonperturbative local physics from a reference solution and builds all parquet diagrams while circumventing potentially divergent irreducible vertices. Its unbiased treatment of different fluctuations is crucial for reproducing the strong-coupling pseudogap in the underdoped Hubbard model, consistent with diagrammatic Monte Carlo calculations. We reveal a strong-coupling spin-fluctuation mechanism of the pseudogap with decisive vertex corrections that encode the enhanced, energy-dependent scattering amplitude between electrons and antiferromagnetic spin fluctuations.

cond-mat.str-el↗
arXiv2026

Spin-Valley Anderson Impurity for Moiré Systems: Fermi Liquid, Pairing, and Pseudogap

Recent experiments support that the magic-angle graphene can be modeled by a periodic array of correlated quantum impurities, immersed in a Dirac sea. This work analytically tackles a spin-valley Anderson impurity, featuring a general (anti-)Hund's interaction ($J_D, J_S$) that can originate from electron-phonon couplings. We derive its full phase diagram, which encompasses rich continuous local phase transitions, and presents a unified origin for pairing potential and pseudogap. In particular, $J_D$ favors a valley doublet, and we show it drives a BKT transition out of heavy Fermi liquid, to an anisotropic doublet phase exhibiting a non-analytic zero-energy kink in the impurity spectral function. $J_S$ drives a second-order transition out of heavy Fermi liquid, to a local singlet phase, with a non-Fermi liquid critical point. We analyze the pairing potential across the phase diagram, and unveil their ubiquitous existence triggered by the (anti-)Hund's multiplet splitting. Crucially, we show the pseudogap shoulders in the spectral function represent multiplet excitations induced by an injected electron or hole. All results are obtained analytically, using techniques including bosonization-refermionization, with further verification by numerical renormalization group calculations. Then we derive the correlation self-energy ansatze that account for pseudogap, and apply to the magic-angle graphene lattice.

cond-mat.str-el↗
arXiv2026

Bosonization Solution to Spin-Valley Kondo Problem: Finite-Size Spectrum and Renormalization Group Analysis

Spin-valley Anderson impurities (SVAIM) with (anti-)Hund's splitting provide a natural explanation to the origin of pairing potential and pseudogap in the magic-angle graphene. In this work, we derive and analytically solve the low-energy Kondo theories for SVAIM at half-filling, with especial focus on the two anti-Hund's regimes: the impurity is either dominated by a valley doublet, or a trivial singlet. In the doublet regime, we reveal that a novel pair Kondo scattering $λ_x$ is required to flip the valley doublet, which involves a quartic operator of bath electrons. Our renormalization group (RG) calculation based on the Coulomb gas analog shows $λ_x$ drives a phase transition of the Berezinskii-Kosterlitz-Thouless type. One side of the transition is an anisotropic doublet phase, characterized by non-universal phase shifts of bath electrons and non-analytic impurity susceptibilities, while the other is a Fermi liquid formed by pair-Kondo resonance. The finite-size many-body spectrum, thermodynamic quantities, and correlation functions for both phases are analytically solved. Remarkably, the solution in the pair-Kondo Fermi liquid is achieved via the constructive approach of bosonization-refermionization along a solvable fixed line, where the many-body interaction $λ_x$ is mapped into a pseudo-fermion bilinear in a rigorous manner. Finally, we also apply the RG analysis to the singlet regime, and identify a second-order phase transition between the Kondo Fermi liquid and a local singlet phase.

cond-mat.str-el↗
arXiv2025

Scalable projected entangled-pair state representation of random quantum circuit states

Classical simulation of a programmable quantum processor is crucial in identifying the threshold of a quantum advantage. We demonstrate the simple update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random quantum circuit states, which center around recent quantum advantage claims. Applied to square lattices of qubits akin to state-of-the-art superconducting processors, the PEPS representation is exact for circuit depths less than $\mathcal{D}_\mathrm{tr}$ = $β\log_2χ$, where $χ$ is the maximum bond dimension and $2 \lesssim β\lesssim 4$ depends on the choice of two-qubit gates, independent of the qubit number $n$. We find the universal scaling behaviors of the state fidelity by treating large-scale circuits of $n \leq 10^{4}$, using $χ\leq 128$ on a conventional CPU. Our method has a polynomial scaling of computational costs with $n$ for circuit depth $\mathcal{D}=O(\log n)$ and is more advantageous than matrix product state approaches if $n$ is large. This work underscores PEPSs as a scalable tool for benchmarking quantum algorithms with future potential for sampling applications using advanced contraction techniques.

quant-ph↗
arXiv2024

Hundness in twisted bilayer graphene: correlated gaps and pairing

We characterize gap-opening mechanisms in the topological heavy fermion (THF) model of magic-angle twisted bilayer graphene (MATBG), with and without electron-phonon coupling, using dynamical mean-field theory (DMFT) with the numerical renormalization group (NRG) impurity solver. In the presence of symmetry breaking associated with valley-orbital ordering (time-reversal-symmetric or Kramers intervalley coherent, or valley polarized), spin anti-Hund and orbital-angular-momentum Hund couplings, induced by the dynamical Jahn-Teller effect, result in a robust pseudogap at filling $2 \lesssim |ν| \lesssim 2.5$. We also find that Hundness enhances the pairing susceptibilities for $1.6 \lesssim |ν| \lesssim 2.8$, which might be a precursor to the superconducting phases neighboring $|ν| = 2$.

cond-mat.str-el↗
arXiv2024

Analytic continuation of multipoint correlation functions

Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more convenient than the KF. However, computing dynamical observables in the MF requires the analytic continuation from imaginary to real frequencies. The analytic continuation is well-known for two-point correlation functions (having one frequency argument), but, for multipoint correlators, a straightforward recipe for deducing all Keldysh components from the MF correlator had not been formulated yet. Recently, a representation of MF and KF correlators in terms of formalism-independent partial spectral functions and formalism-specific kernels was introduced by Kugler, Lee, and von Delft [Phys. Rev. X 11, 041006 (2021)]. We use this representation to formally elucidate the connection between both formalisms. We show how a multipoint MF correlator can be analytically continued to recover all partial spectral functions and yield all Keldysh components of its KF counterpart. The procedure is illustrated for various correlators of the Hubbard atom.

cond-mat.str-el↗
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 $ω/T$ 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${}_5$.

cond-mat.str-el↗
arXiv2024

Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG.Due to the overcompleteness, we achieve only qualitative agreement.

cond-mat.str-el↗
arXiv2024

Symmetric improved estimators for multipoint vertex functions

Multipoint vertex functions, and the four-point vertex in particular, are crucial ingredients in many-body theory. Recent years have seen significant algorithmic progress toward numerically computing their dependence on multiple frequency arguments. However, such computations remain challenging and are prone to suffer from numerical artifacts, especially in the real-frequency domain. Here, we derive estimators for multipoint vertices that are numerically more robust than those previously available. We show that the two central steps for extracting vertices from correlators, namely the subtraction of disconnected contributions and the amputation of external legs, can be achieved accurately through repeated application of equations of motion, in a manner that is symmetric with respect to all frequency arguments and involves only fully renormalized objects. The symmetric estimators express the core part of the vertex and all asymptotic contributions through separate expressions that can be computed independently, without subtracting the large-frequency limits of various terms with different asymptotic behaviors. Our strategy is general and applies equally to the Matsubara formalism, the real-frequency zero-temperature formalism, and the Keldysh formalism. We demonstrate the advantages of the symmetric improved estimators by computing the Keldysh four-point vertex of the single-impurity Anderson model using the numerical renormalization group.

cond-mat.str-el↗
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.

cond-mat.str-el↗
arXiv2022

Tuning orbital-selective phase transitions in a two-dimensional Hund's correlated system

Hund's rule coupling ($\textit{J}$) has attracted much attention recently for its role in the description of the novel quantum phases of multi orbital materials. Depending on the orbital occupancy, $\textit{J}$ can lead to various intriguing phases. However, experimental confirmation of the orbital occupancy dependency has been difficult as controlling the orbital degrees of freedom normally accompanies chemical inhomogeneities. Here, we demonstrate a method to investigate the role of orbital occupancy in $\textit{J}$ related phenomena without inducing inhomogeneities. By growing SrRuO$_3$ monolayers on various substrates with symmetry-preserving interlayers, we gradually tune the crystal field splitting and thus the orbital degeneracy of the Ru $\textit{t$_2$$_g$}$ orbitals. It effectively varies the orbital occupancies of two-dimensional (2D) ruthenates. Via in-situ angle-resolved photoemission spectroscopy, we observe a progressive metal-insulator transition (MIT). It is found that the MIT occurs with orbital differentiation: concurrent opening of a band insulating gap in the $\textit{d$_x$$_y$}$ band and a Mott gap in the $\textit{d$_x$$_z$$_/$$_y$$_z$}$ bands. Our study provides an effective experimental method for investigation of orbital-selective phenomena in multi-orbital materials.

cond-mat.str-el↗
arXiv2021

Multipoint correlation functions: spectral representation and numerical evaluation

The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The connection between results obtained in either way is made through spectral (or Lehmann) representations, well known for two-point correlation functions. Here, we complete this picture by deriving generalized spectral representations for multipoint correlation functions that apply in all of the commonly used many-body frameworks: the imaginary-frequency Matsubara and the real-frequency zero-temperature and Keldysh formalisms. Our approach separates spectral from time-ordering properties and thereby elucidates the relation between the three formalisms. The spectral representations of multipoint correlation functions consist of partial spectral functions and convolution kernels. The former are formalism independent but system specific; the latter are system independent but formalism specific. Using a numerical renormalization group (NRG) method described in the accompanying paper, we present numerical results for selected quantum impurity models. We focus on the four-point vertex (effective interaction) obtained for the single-impurity Anderson model and for the dynamical mean-field theory (DMFT) solution of the one-band Hubbard model. In the Matsubara formalism, we analyze the evolution of the vertex down to very low temperatures and describe the crossover from strongly interacting particles to weakly interacting quasiparticles. In the Keldysh formalism, we first benchmark our results at weak and infinitely strong interaction and then reveal the rich real-frequency structure of the DMFT vertex in the coexistence regime of a metallic and insulating solution.

cond-mat.str-el↗
arXiv2021

Computing local multipoint correlators using the numerical renormalization group

Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In the accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group (NRG) approach, capable of efficiently evaluating these spectral representations, to compute local three- and four-point correlators of quantum impurity models. The key objects in our scheme are partial spectral functions, encoding the system's dynamical information. Their computation via NRG allows us to simultaneously resolve various multiparticle excitations down to the lowest energies. By subsequently convolving the partial spectral functions with appropriate kernels, we obtain multipoint correlators in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms. We present exemplary results for the connected four-point correlators of the Anderson impurity model, and for resonant inelastic x-ray scattering (RIXS) spectra of related impurity models. Our method can treat temperatures and frequencies -- imaginary or real -- of all magnitudes, from large to arbitrarily small ones.

cond-mat.str-el↗
arXiv2020

Non-Fermi-liquid Kondo screening under Rabi driving

We investigate a Rabi-Kondo model describing an optically driven two-channel quantum dot device featuring a non-Fermi-liquid Kondo effect. Optically induced Rabi oscillation between the valence and conduction levels of the dot gives rise to a two-stage Kondo effect: Primary screening of the local spin is followed by secondary nonequilibrium screening of the local orbital degree of freedom. Using bosonization arguments and the numerical renormalization group, we compute the dot emission spectrum and residual entropy. Remarkably, both exhibit two-stage Kondo screening with non-Fermi-liquid properties at both stages.

cond-mat.mes-hall↗
arXiv2020

Orbital differentiation in Hund metals

Orbital differentiation is a common theme in multiorbital systems, yet a complete understanding of it is still missing. Here, we consider a minimal model for orbital differentiation in Hund metals with a highly accurate method: We use the numerical renormalization group as a real-frequency impurity solver for a dynamical mean-field study of three-orbital Hubbard models, where a crystal field shifts one orbital in energy. The individual phases are characterized with dynamic correlation functions and their relation to diverse Kondo temperatures. Upon approaching the orbital-selective Mott transition, we find a strongly suppressed spin coherence scale and uncover the emergence of a singular Fermi liquid and interband doublon-holon excitations. Our theory describes the diverse polarization-driven phenomena in the $t_{2g}$ bands of materials such as ruthenates and iron-based superconductors, and our methodological advances pave the way towards real-frequency analyses of strongly correlated materials.

cond-mat.str-el↗