arXiv subjects

Örs Legeza

Publications and source records attributed to Örs Legeza.

At least 37 records · Page 2Linked to original sources

arXiv2023

Boosting the effective performance of massively parallel tensor network state algorithms on hybrid CPU-GPU based architectures via non-Abelian symmetries

We present novel algorithmic solutions together with implementation details utilizing non-Abelian symmetries in order to boost the current limits of tensor network state algorithms on high performance computing infrastructure. In our in-house developed hybrid CPU-multiGPU solution scheduling is decentralized, threads are autonomous and inter-thread communications are solely limited to interactions with globally visible lock-free constructs. Our custom tailored virtual memory management ensures data is produced with high spatial locality, which together with the use of specific sequences of strided batched matrix operations translates to significantly higher overall throughput. In order to lower IO overhead, an adaptive buffering technique is used to dynamically match the level of data abstraction, at which cache repositories are built and reused, to system resources. The non-Abelian symmetry related tensor algebra based on Wigner-Eckhart theorem is fully detached from the conventional tensor network layer, thus massively parallel matrix and tensor operations can be performed without additional overheads. Altogether, we have achieved an order of magnitude increase in performance with respect to results reported in arXiv:2305.05581 in terms of computational complexity and at the same time a factor of three to six in the actual performance measured in TFLOPS. Benchmark results are presented on Hilbert space dimensions up to $2.88\times10^{36}$ obtained via large-scale SU(2) spin adapted density matrix renormalization group simulations on selected strongly correlated molecular systems. These demonstrate the utilization of NVIDIA's highly specialized tensor cores, leading to performance around 110 TFLOPS on a single node supplied with eight NVIDIA A100 devices. In comparison to U(1) implementations with matching accuracy, our solution has an estimated effective performance of 250-500 TFLOPS.

physics.comp-ph↗

arXiv2023

Generic Mott-Hubbard phase diagram for extended Hubbard models without Umklapp scattering

We determine the ground-state phase diagram for the 1/r-Hubbard model with repulsive nearest-neighbor interaction at half band-filling using the density-matrix renormalization group (DMRG) method. Due to the absence of Umklapp cattering, the phase diagram displays finite regions for the three generic phases, namely, a Luttinger liquid metal for weak interactions, a Mott-Hubbard insulator for dominant Hubbard interactions, and a charge-density-wave insulator for dominant nearest-neighbor interactions. Up to moderate interactions strengths, the quantum phase transitions between the metallic and insulating phases are continuous, i.e., the gap opens continuously as a function of the interaction strength. We conclude that generic short-range interactions do not change the nature of the Mott transition qualitatively.

cond-mat.str-el↗

arXiv2023

Massively Parallel Tensor Network State Algorithms on Hybrid CPU-GPU Based Architectures

The interplay of quantum and classical simulation and the delicate divide between them is in the focus of massively parallelized tensor network state (TNS) algorithms designed for high performance computing (HPC). In this contribution, we present novel algorithmic solutions together with implementation details to extend current limits of TNS algorithms on HPC infrastructure building on state-of-the-art hardware and software technologies. Benchmark results obtained via large-scale density matrix renormalization group (DMRG) simulations are presented for selected strongly correlated molecular systems addressing problems on Hilbert space dimensions up to $2.88\times10^{36}$.

quant-ph↗

arXiv2023

Predicting the FCI energy of large systems to chemical accuracy from restricted active space density matrix renormalization group calculations

We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [arXiv:2111.06665] in electronic structure calculations. This yields a new extrapolation method, DMRG-RAS-X, which reaches chemical accuracy for strongly correlated systems such as the Chromium dimer, dicarbon up to a large cc-pVQZ basis, and even a large chemical complex like the FeMoco with significantly lower computational demands than previous methods. The method is free of empirical parameters, performed robustly and reliably in all examples we tested, and has the potential to become a vital alternative method for electronic structure calculations in quantum chemistry, and more generally for the computation of strong correlations in nuclear and condensed matter physics.

physics.chem-ph↗

arXiv2023

Symmetric carbon tetramers forming chemically stable spin qubits in hBN

Point defect quantum bits in semiconductors have the potential to revolutionize sensing at atomic scales. Currently, vacancy related defects, such as the NV center in diamond and the VB$^-$ in hexagonal boron nitride (hBN), are at the forefront of high spatial resolution and low dimensional sensing. On the other hand, vacancies' reactive nature and instability at the surface limit further developments. Here, we study the symmetric carbon tetramers in hBN and propose them as a chemically stable spin qubit for sensing in low dimensions. We utilize periodic-DFT and quantum chemistry approaches to reliably and accurately predict the electronic, optical, and spin properties of the studied defect. We show that the nitrogen centered symmetric carbon tetramer gives rise to spin state dependent optical signals with strain sensitive intersystem crossing rates. Furthermore, the weak hyperfine coupling of the defect to their spin environments results in a reduced electron spin resonance linewidth that may enhance sensitivity.

cond-mat.mtrl-sci↗

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

Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions

We investigate the charge-density wave (CDW) transition for one-dimensional spinless fermions at half band-filling with nearest-neighbor electron transfer amplitude $t$ and interaction $V$. The model is equivalent to the anisotropic XXZ Heisenberg model for which the Bethe Ansatz provides an exact solution. For $V> V_{\rm c}= 2t$, the CDW order parameter and the single-particle gap are finite but exponentially small, as is characteristic for a Kosterlitz-Thouless transition. It is notoriously difficult to locate such infinite-order phase transitions in the phase diagram using approximate analytical and numerical approaches. Second-order Hartree-Fock theory is qualitatively applicable for all interaction strengths, and predicts the CDW transition to occur at $V_{\rm c,2}^{(2)}\approx 1.5t$. Second-order Hartree Fock theory is almost variational because the density of quasi-particle excitations is small. We apply the density-matrix renormalization group (DMRG) for periodic boundary conditions for system sizes up to 514 sites which permits a reliable extrapolation of all physical quantities to the thermodynamic limit, apart from the critical region. We investigate the ground-state energy, the gap, the order parameter, the momentum distribution, the quasi-particle density, and the density-density correlation function to locate $V_{\rm c}$ from the DMRG data. Tracing the breakdown of the Luttinger liquid and the peak in the quasi-particle density at the band edge permits us to reproduce $V_{\rm c}$ with an accuracy of one percent.

cond-mat.str-el↗

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↗

arXiv2022

Compressing multireference character of wave functions via fermionic mode optimization

In this work, we present a brief overview of the fermionic mode optimization within the framework of tensor network state methods [PRL 117,210402(2016)], and demonstrate that it has the potential to compress the multireference character of the wave functions after finding optimal molecular orbitals (modes), based on entanglement minimization. Numerical simulations have been performed for the nitrogen dimer in the cc-pVDZ basis for the equilibrium and for stretched geometries.

physics.chem-ph↗

arXiv2022

Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite basis limit

In this article we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density matrix renormalization group method by computing the core-valence entanglement in the C$_2$ ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.

quant-ph↗

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

Fermionic systems for quantum information people

The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan--Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.

quant-ph↗

arXiv2021

Quantum sensor in a single layer van der Waals material

Point defect qubits in semiconductors have demonstrated their outstanding high spatial resolution sensing capabilities of broad multidisciplinary interest. Two-dimensional (2D) semiconductors hosting such sensors have recently opened up new horizons for sensing in the subnanometer scales in 2D heterostructures. However, controlled creation of quantum sensor in a single layer 2D materials with high sensitivity has been elusive so far. Here, we report on a novel 2D quantum sensor, the VB2 centre in hexagonal boron nitride (hBN), with superior sensing capabilities. The centre's inherently low symmetry configuration gives rise to unique electronic and spin properties that implement a qubit in a 2D material with unprecedented sensitivity. The qubit is decoupled from its dense spin environment at low magnetic fields that gives rise to the reduction of the spin resonance linewidth and elongation of the coherence time. The VB2 centre is also equipped with a classical memory that can be utilized in storing population information. Using scanning transmission electron microscopy imaging, we confirm the presence of the point defect structure in free standing monolayer hBN created by electron beam irradiation. Our results provide a new material solution towards atomic-scale sensing in low dimensions.

cond-mat.mes-hall↗

arXiv2021

Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

We apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction~$U$ equals the band width, $U_{\rm c}=W$, where the single-particle gap opens linearly, $Δ(U\geq W)=U-W$. The simple nature of the elementary excitations permits to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_{\rm F}=0$ cannot be used to locate accurately $U_{\rm c}$ from finite-size systems. However, the slope of $n_k$ at the band edges, $k_{\rm B}=\pm π$, reveals the formation of a single-particle bound state which can be used to determine $U_{\rm c}$ reliably from $n_k$ using accurate finite-size data.

cond-mat.str-el↗

arXiv2021

Assessing the accuracy of tailored coupled cluster methods corrected by electronic wave functions of polynomial cost

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various tailored coupled cluster methods externally corrected by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled-cluster (fpCC) methods, which are externally corrected by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N$_2$, F$_2$, C$_2$, CN$^+$, BN, BO$^+$, and Cr$_2$) and molecules (ammonia, ethylene, cyclobutadiene, benzene) for which conventional single-reference coupled cluster singles and doubles (CCSD) is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to multireference and/or experimental reference data and generally outrank the conventional single-reference CCSD approach. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

physics.chem-ph↗

arXiv2021

How creating one additional well can generate Bose-Einstein condensation

The realization of Bose-Einstein condensation in ultracold trapped gases has led to a revival of interest in that fascinating quantum phenomenon. This experimental achievement necessitated both extremely low temperatures and sufficiently weak interactions. Particularly in reduced spatial dimensionality even an infinitesimal interaction immediately leads to a departure to quasi-condensation. We propose a system of strongly interacting bosons which overcomes those obstacles by exhibiting a number of intriguing related features: (i) The tuning of just a single control parameter drives a transition from quasi-condensation to complete condensation, (ii) the destructive influence of strong interactions is compensated by the respective increased mobility, (iii) topology plays a crucial role since a crossover from one- to `infinite'-dimensionality is simulated, (iv) a ground state gap opens which makes the condensation robust to thermal noise. Remarkably, all these features can be derived by analytical and exact numerical means despite the non-perturbative character of the system.

cond-mat.quant-gas↗

arXiv2021

Topologically protected, correlated end spin formation in carbon nanotubes

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogues of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, as well as the size of the end spins: for $S=1/2$ end spins their interaction is antiferromagnetic, while for $S>1/2$ it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

cond-mat.str-el↗

arXiv2020

Quantum Quench and Charge Oscillations in the SU(3) Hubbard Model: a Test of Time Evolving Block Decimation with general non-Abelian Symmetries

We introduce the notion of non-Abelian tensors, and use them to construct a general non-Abelian time evolving block decimation (NA-TEBD) scheme that uses an arbitrary number of Abelian and non-Abelian symmetries. Our approach increases the speed and memory storage efficiency of matrix product state based computations by several orders of magnitudes, and makes large bond dimensions accessible even on simple desktop architectures. We use it to study post-quench dynamics in the repulsive SU(3) Hubbard model, and to determine the time evolution of various local operators and correlation functions efficiently. Interactions turn algebraic charge relaxation into exponential, and suppress coherent quantum oscillations rapidly.

cond-mat.str-el↗