arXiv subjects

Miklós Antal Werner

Publications and source records attributed to Miklós Antal Werner.

At least 19 recordsLinked to original sources

arXiv2026

Diversifying time evolution of matrix product states using BUGs

Time evolution of tensor-network states is a central tool for studying nonequilibrium dynamics in strongly correlated quantum systems. In the past decade, using the time-dependent variational principle (TDVP) discretized by projector-splitting has become the gold standard for evolving matrix product states (MPS) with long-range Hamiltonians. More recently, a conceptually different class of discretizations of the TDVP, the class of Basis Update and Galerkin (BUG) integrators, has been developed within the framework of dynamical low-rank approximation, offering an alternative, more flexible approach. In this work, we formulate two BUG integrators explicitly for MPS. The BUG integrators result in "single-site" MPS integrators that are robust with respect to small singular values, avoid backward-in-time substeps, and naturally allow for the adaptive choice of bond dimensions. We consider the augmented BUG integrator of first order and the midpoint BUG integrator of second order and clarify their relation to the projector-splitting discretization of the TDVP. Using representative models of strongly correlated quantum systems, like the XY spin model with long-range interaction and two-dimensional lattice models of fermions and spins of various lengths, we perform a systematic numerical comparison between BUG and projector-splitting time discretizations of the continuous-time TDVP, focusing on scalability, numerical complexity, and accuracy. We find that BUG integrators, due to their reduced numerical cost and the flexibility of the concept, provide a competitive and, in certain regimes, advantageous alternative to the well-established time-stepping by projector-splitting in TDVP, especially in models with large local dimensions, and in cases where observables are extracted with high temporal resolution.

cond-mat.str-el↗

arXiv2026

Block entropy area based non-local fermionic mode optimization with gradient disentanglers

We introduce a systematic block entropy area based mode optimization algorithm for many-body quantum states of interacting fermions represented by matrix product states. From the gradient of a global cost function, the block entropy area, a long-ranged, non-interacting effective disentangler Hamiltonian is formed. We then simulate the time-dependent Schrödinger equation driven by the disentangler Hamiltonian by employing the time-dependent variational principle based on projector splitting, and minimize the cost function. The combination of the density matrix renormalization group with this gradient-based entanglement minimization forms an efficient low-rank iterative ground-state algorithm that also provides an optimized single-particle basis for matrix product state representation. We demonstrate the method on two-dimensional lattice models of interacting fermions and the Fe${_4}$S${_4}$ cluster, and show its robustness and superiority over earlier protocols using nearest-neighbor mode rotations and reorderings.

cond-mat.str-el↗

arXiv2026

Global fermionic mode optimization via swap gates

An optimal choice of single-particle modes leads to an optimal tensor network-based compression of the many-body wave function for systems of indistinguishable particles, which compression can be essential for large, close-to-critical systems. The proposed mode optimization relies on the minimization of the block entropy area, a global quantity that measures entanglement of the wave function along the one-dimensional chain of modes. Extension of the two-site DMRG algorithm by nearest-neighbor mode optimizations is straightforward, but it performs poorly without systematic reordering of modes. Moreover, finding a stationary optimal point in the combination of the fixed-rank MPS manifold and the unitary group of mode rotations requires optimization for every generator, i.e., for every two-mode pair. Here, a systematic joint optimization protocol over the MPS manifold and the full unitary group is presented in which every two-mode pair is accessed by a carefully constructed sequence of two-qubit operations, including swap-gate controlled permutations. Large-scale DMRG simulations of strongly correlated two-dimensional fermionic lattice models and the multireference Fe$_4$S$_4$ transition metal cluster demonstrate rapid convergence towards the optimum, achieving low energy and low entanglement.

cond-mat.str-el↗

arXiv2026

Hunting for quantum advantage in electronic structure calculations is a highly non-trivial task

In light of major developments over the past decades in both quantum computing and simulations on classical hardware, it is a serious challenge to identify a real-world problem where quantum advantage is expected to appear. In quantum chemistry, electronic structure calculations of strongly correlated, i.e. multi-reference problems, are often argued to fall into such category because of their intractability with standard methods based on mean-field theory. Therefore, providing state-of-the-art benchmark data by classical algorithms is necessary to make a decisive conclusion when such competing development directions are compared. We report cutting-edge performance results together with high accuracy ground state energy for the Fe$_4$S$_4$ molecular cluster on a CAS(54,36) model space, a problem that has been included quite recently among the list of systems in the {\it Quantum Advantage Tracker} webpage maintained by IBM and RIKEN. Pushing the limits even further, we also present CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 89 electrons in 102 orbitals [CAS(89,102)] for the Fe$_5$S$_{12}$H$_4^{5-}$ molecular system comprising twenty five open shell orbitals in its sextet ground state and an active spaces size of 331 electrons in 451 orbitals. We have achieved our results via mixed-precision spin-adapted \textit{ab initio} Density Matrix Renormalization Group (DMRG) electronic structure calculations interfaced with the ORCA program package and utilizing the NVIDIA Blackwell graphics processing unit (GPU) platform. We argue that DMRG benchmark data should be taken as a classical reference when quantum advantage is reported. In addition, full exploitation of classical hardware should also be considered since even the most advanced DMRG implementations are still in a premature stage regarding utilization of all the benefits of GPU technology.

physics.chem-ph↗

arXiv2025

Real-Time Dynamics in a (2+1)-D Gauge Theory: The Stringy Nature on a Superconducting Quantum Simulator

Understanding the confinement mechanism in gauge theories and the universality of effective string-like descriptions of gauge flux tubes remains a fundamental challenge in modern physics. We probe string modes of motion with dynamical matter in a digital quantum simulation of a (2+1) dimensional gauge theory using a superconducting quantum processor with up to 144 qubits, stretching the hardware capabilities with quantum-circuit depths comprising up to 192 two-qubit layers. We realize the $Z_2$-Higgs model ($Z_2$HM) through an optimized embedding into a heavy-hex superconducting qubit architecture, directly mapping matter and gauge fields to vertex and link superconducting qubits, respectively. Using the structure of local gauge symmetries, we implement a comprehensive suite of error suppression, mitigation, and correction strategies to enable real-time observation and manipulation of electric strings connecting dynamical charges. Our results resolve a dynamical hierarchy of longitudinal oscillations and transverse bending at the end points of the string, which are precursors to hadronization and rotational spectra of mesons. We further explore multi-string processes, observing the fragmentation and recombination of strings. The experimental design supports 300,000 measurement shots per circuit, totaling 600,000 shots per time step, enabling high-fidelity statistics. We employ extensive tensor network simulations using the basis update and Galerkin method to predict large-scale real-time dynamics and validate our error-aware protocols. This work establishes a milestone for probing non-perturbative gauge dynamics via superconducting quantum simulation and elucidates the real-time behavior of confining strings.

quant-ph↗

arXiv2025

Orbital optimization of large active spaces via AI-accelerators

We present an efficient orbital optimization procedure that combines the highly GPU accelerated, spin-adapted density matrix renormalization group (DMRG) method with the complete active space self-consistent field (CAS-SCF) approach for quantum chemistry implemented in the ORCA program package. Leveraging the computational power of the latest generation of Nvidia GPU hardware, we perform CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 82 electrons in 82 orbitals [CAS(82,82)] in molecular systems comprising of active spaces sizes of hundreds of electrons in thousands of orbitals. For both the NVIDIA DGX-A100 and DGX-H100 hardware, we provide a detailed scaling and error analysis of our DMRG-SCF approach for benchmark systems consisting of polycyclic aromatic hydrocarbons and iron-sulfur complexes of varying sizes. Our efforts demonstrate for the first time that highly accurate DMRG calculations at large bond dimensions are critical for obtaining reliably converged CAS-SCF energies. For the more challenging iron-sulfur benchmark systems, we furthermore find the optimized orbitals of a converged CAS-SCF calculation to depend more sensitively on the DMRG parameters than those for the polycyclic aromatic hydrocarbons. The ability to obtain converged CAS-SCF energies and orbitals for active spaces of such large sizes within days reduces the challenges of including the appropriate orbitals into the CAS or selecting the correct minimal CAS, and may open up entirely new avenues for tackling strongly correlated molecular systems.

physics.chem-ph↗

arXiv2025

Tensor network state methods and quantum information theory for strongly correlated molecular systems

A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic mode optimization, i.e., a general approach to find an optimal matrix product state (MPS) parametrization of a quantum many-body wave function with the minimum number of parameters for a given error margin, the restricted active space DMRG-RAS-X method, multi-orbital correlations and entanglement, developments on hybrid CPU-multiGPU parallelization, and an efficient treatment of non-Abelian symmetries on high-performance computing (HPC) infrastructures. Scaling analysis on NVIDIA DGX-A100 platform is also presented.

cond-mat.str-el↗

arXiv2024

Loss-induced quantum information jet in an infinite temperature Hubbard chain

Information propagation in the one-dimensional infinite temperature Hubbard model with a dissipative particle sink at the end of a semi-infinite chain is studied. In the strongly interacting limit, the two-site mutual information and the operator entanglement entropy exhibit a rich structure with two propagating information fronts and superimposed interference fringes. A classical reversible cellular automaton model quantitatively captures the transport and the slow, classical part of the correlations, but fails to describe the rapidly propagating information jet. The fast quantum jet resembles coherent free particle propagation, with the accompanying long-ranged interference fringes that are exponentially damped by short-ranged spin correlations in the many-body background.

cond-mat.str-el↗

arXiv2024

Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains

We propose a numerical method to efficiently compute quantum generating functions (QGF) for a wide class of observables in one-dimensional quantum systems at high temperature. We obtain high-accuracy estimates for the cumulants and reconstruct full counting statistics from the QGF. We demonstrate its potential on spin $S=1/2$ anisotropic Heisenberg chain, where we can reach time scales hitherto inaccessible to state-of-the-art classical and quantum simulations. Our results challenge the conjecture of the Kardar--Parisi--Zhang universality for isotropic integrable quantum spin chains.

cond-mat.stat-mech↗

arXiv2024

Collective tunneling of a Wigner necklace in carbon nanotubes

The collective tunneling of a Wigner necklace - a crystal-like state of a small number of strongly interacting electrons confined to a suspended nanotube and subject to a double well potential - is theoretically analyzed and compared with experiments in [Shapir \emph{et al.}, Science {\bf 364}, 870 (2019)]. Density Matrix Renormalization Group computations, exact diagonalization, and instanton theory provide a consistent description of this very strongly interacting system, and show good agreement with experiments. Experimentally extracted and theoretically computed tunneling amplitudes exhibit a scaling collapse. Collective quantum fluctuations renormalize the tunneling, and substantially enhance it as the number of electrons increases.

cond-mat.mes-hall↗

arXiv2024

Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method

We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art high performance computing infrastructures. We demonstrate for the two dimensional spinless fermion model and for the Hubbard model on torus geometry that altogether several orders of magnitude in computational time can be saved by performing calculations on an optimized basis and by utilizing hybrid CPU-multiGPU parallelization. At least an order of magnitude reduction in computational complexity results from mode optimization, while a further order of reduction in wall time is achieved by massive parallelization. Our results are measured directly in FLOP and seconds. A detailed scaling analysis of the obtained performance as a function of matrix ranks and as a function of system size up to $12\times 12$ lattice topology is discussed. Our CPU-multiGPU model also tremendously accelerates the calculation of the one- and two-particle reduced density matrices, which can be used to construct various order parameters and trace quantum phase transitions with high fidelity.

cond-mat.str-el↗

arXiv2023

Multiparticle quantum walk: a dynamical probe of topological many-body excitations

Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting $N$ particles with multiple flavors in the interacting SU$(N)$ Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the $N$-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.

quant-ph↗

arXiv2023

Kardar-Parisi-Zhang scaling in the Hubbard model

We explore the Kardar-Parisi-Zhang (KPZ) scaling in the one-dimensional Hubbard model, which exhibits global $SU_c(2)\otimes SU_s(2)$ symmetry at half-filling, for the pseudo-charge and the total spin. We analyze dynamical scaling properties of high temperature charge and spin correlations and transport. At half-filling, we observe a clear KPZ scaling in both charge and spin sectors. Away from half-filling, the $SU_c(2)$ charge symmetry is reduced to $U_c(1)$, while the $SU_s(2)$ symmetry for the total spin is retained. Consequently, transport in the charge sector becomes ballistic, while KPZ scaling is preserved in the spin sector. These findings confirm the link between non-abelian symmetries and KPZ scaling in the presence of integrability. We study two settings of the model: one involving a quench from a bi-partitioned state asymptotically close to the $T=\infty$ equilibrium state of the system, and another where the system is coupled to two markovian reservoirs at the two edges of the chain.

cond-mat.str-el↗

arXiv2023

Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model

We investigate the quantum quench dynamics of the interacting Hatano-Nelson model with open boundary conditions using both abelian bosonization and numerical methods. Specifically, we follow the evolution of the particle density and current profile in real space over time by turning the imaginary vector potential on or off in the presence of weak interactions. Our results reveal spatio-temporal Friedel oscillations in the system with light cones propagating ballistically from the open ends, accompanied by local currents of equal magnitude for both switch off and on protocols. Remarkably, the bosonization method accurately accounts for the density and current patterns with a single overall fitting parameter. The continuity equation is satisfied by the long wavelength part of the density and current, despite the non-unitary time evolution when the Hatano-Nelson term is switched on.

cond-mat.str-el↗

arXiv2022

Towards large-scale restricted active space calculations inspired by the Schmidt decomposition

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C$_2$ and Cr$_2$, which are notorious for their multi-reference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.

physics.chem-ph↗

arXiv2022

Spectroscopic evidence for engineered hadron formation in repulsive fermionic $\textrm{SU}(N)$ Hubbard Models

Particle formation represents a central theme in various branches of physics, often associated to confinement. Here we show that dynamical hadron formation can be spectroscopically detected in an ultracold atomic setting within the most paradigmatic and simplest model of condensed matter physics, the repulsive $\textrm{SU}(N)$ Hubbard model. By starting from an appropriately engineered initial state of the ${{\textrm{SU}(3)}}$ Hubbard model, not only mesons (doublons) but also baryons (trions) are naturally generated during the time evolution. In the strongly interacting limit, baryons become heavy and attract each other strongly, and their residual interaction with mesons generates meson diffusion, as captured by the evolution of the equal time density correlation function. Hadrons remain present in the long time limit, while the system thermalizes to a negative temperature state. Our conclusions extend to a large variety of initial conditions, all spatial dimensions, and for SU($N>2$) Hubbard models.

cond-mat.stat-mech↗

arXiv2021

Simulating Lindbladian evolution with non-abelian symmetries: Ballistic front propagation in the $SU(2)$ Hubbard model with a localized loss

We develop a non-Abelian time evolving block decimation (NA-TEBD) approach to study of open systems governed by Lindbladian time evolution, while exploiting an arbitrary number of abelian or non-abelian symmetries. We illustrate this method in a one-dimensional fermionic $SU(2)$ Hubbard model on a semi-infinite lattice with localized particle loss at one end. We observe a ballistic front propagation with strongly renormalized front velocity, and a hydrodynamic current density profile. For large loss rates, a suppression of the particle current is observed, as a result of the quantum Zeno effect. Operator entanglement is found to propagate faster than the depletion profile, preceding the latter.

cond-mat.str-el↗

arXiv2021

The fate of the Kondo cloud in a superconductor

Magnetic impurities embedded in a metal are screened by the Kondo effect, signaled by the formation of an extended correlation cloud, the so-called Kondo or screening cloud. In a superconductor, the Kondo state turns into sub-gap Yu-Shiba-Rusinov (Shiba) states, and a quantum phase transition occurs between screened and unscreened phases once the superconducting energy gap $Δ$ becomes sufficiently large compared to the Kondo temperature, $T_K$. Here we show that, although the Kondo state does not form in the unscreened phase, the Kondo cloud does exist in both quantum phases. However, while screening is complete in the screened phase, it is only partial in the unscreened phase. Compensation, a quantity introduced to characterize the integrity of the cloud, is universal, and shown to be related to the magnetic impurities' $g$-factor, monitored experimentally by bias spectroscopy.

cond-mat.str-el↗