arXiv subjects

Garnet K. -L. Chan

Publications and source records attributed to Garnet K. -L. Chan.

9 recordsLinked to original sources

arXiv2026

Efficient Application of Tensor Network Operators to Tensor Network States Through Successive Deterministic Compression

We introduce an algorithm to apply tree tensor network operators to tree tensor network states followed by compression. Especially when applying a matrix product operator to matrix product states, this serves as a key subroutine in tensor network algorithms. We name the method successive deterministic compression (SDC). We compare SDC to existing operator application and compression algorithms in benchmarks involving random tensor network operators and states, as well as circuit simulation with standard entangling gates. We find that successive deterministic compression is consistently among the best-performing techniques when the tensor network state (after the operator application) is not highly compressible. Our results also highlight the flexibility of general tree tensor network structures for simulating circuits with long-range entanglement.

quant-ph↗

arXiv2024

Fast emulation of fermionic circuits with matrix product states

We describe a matrix product state (MPS) extension for the Fermionic Quantum Emulator (FQE) software library. We discuss the theory behind symmetry adapted matrix product states for approximating many-body wavefunctions of spin-1/2 fermions, and we present an open-source, MPS-enabled implementation of the FQE interface (MPS-FQE). The software uses the open-source pyblock3 and block2 libraries for most elementary tensor operations, and it can largely be used as a drop-in replacement for FQE that allows for more efficient, but approximate, emulation of larger fermionic circuits. Finally, we show several applications relevant to both near-term and fault-tolerant quantum algorithms where approximate emulation of larger systems is expected to be useful: characterization of state preparation strategies for quantum phase estimation, the testing of different variational quantum eigensolver Ansätze, the numerical evaluation of Trotter errors, and the simulation of general quantum dynamics problems. In all these examples, approximate emulation with MPS-FQE allows us to treat systems that are significantly larger than those accessible with a full statevector emulator.

quant-ph↗

arXiv2020

Exploring the magnetic properties of the largest single molecule magnets

The giant $\{ \mathrm{Mn}_{70} \}$ and $\{ \mathrm{Mn}_{84} \}$ wheels are the largest nuclearity single-molecule magnets synthesized to date and understanding their magnetic properties poses a challenge to theory. Starting from first principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled $\{ \mathrm{Mn}_{7} \}$ subunits carrying an effective $S=2$ spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest energy excitations arising from Heisenberg-ring-like excitations of the $\{ \mathrm{Mn}_{7} \}$ subunits around the wheel, at energies consistent with the observed temperature dependence of the magnetic susceptibility. We further suggest an important role for weak longer-range couplings in selecting the precise spin ground-state of the $\mathrm{Mn}$ wheels out of the nearly degenerate ground-state band.

physics.chem-ph↗

arXiv2018

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance (EPR) $g$-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute $g$-tensors for the \ce{TiF3} and \ce{CuCl4^2-} complexes, a [2Fe-2S] model of the active center of ferredoxins, and a \ce{Mn4CaO5} model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining $g$-tensors in multireference calculations with a large number of open shells.

physics.chem-ph↗

arXiv2017

Automated construction of molecular active spaces from atomic valence orbitals

We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multi-configuration and multireference (MR) electronic structure calculations. Concretely, the technique constructs active molecular orbitals capable of describing all relevant electronic configurations emerging from a targeted set of atomic valence orbitals (e.g., the metal d orbitals in a coordination complex). This is achieved via a linear transformation of the occupied and unoccupied orbital spaces from an easily obtainable single-reference wavefunction (such as from a Hartree-Fock or Kohn-Sham calculations) based on projectors to targeted atomic valence orbitals. We discuss the premises, theory, and implementation of the idea, and several of its variations are tested. To investigate the performance and accuracy, we calculate the excitation energies for various transition metal complexes in typical application scenarios. Additionally, we follow the homolytic bond breaking process of a Fenton reaction along its reaction coordinate. While the described AVAS technique is not an universal solution to the active space problem, its premises are fulfilled in many application scenarios of transition metal chemistry and bond dissociation processes. In these cases the technique makes MR calculations easier to execute, easier to reproduce by any user, and simplifies the determination of the appropriate size of the active space required for accurate results.

physics.chem-ph↗

arXiv2016

Five years of density matrix embedding theory

Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. In contrast to most embedding methods, DMET explicitly allows for quantum entanglement between both. In this chapter, we discuss both the ground-state and response theory formulations of DMET, and review several applications. In addition, a proof is given that the local density of states can be obtained by working with a Fock space of bath orbitals.

cond-mat.str-el↗

arXiv2016

A time-dependent formulation of multi-reference perturbation theory

We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting t-NEVPT2 method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules, and outline directions for the future.

physics.chem-ph↗

arXiv2009

Perfect Reflection of Chiral Fermions in Gated Graphene Nanoribbons

We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a non-equilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find \emph{perfect reflection} of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.

cond-mat.mes-hall↗

arXiv2007

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as β-carotene, correlating with near-exact accuracy the optimised complete π-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.

cond-mat.str-el↗