Exploring Ground and Excited States via Single Reference Coupled-Cluster Theory and Algebraic Geometry

• URL: http://arxiv.org/abs/2405.12238v2
• Date: Tue, 10 Sep 2024 21:40:24 GMT
• Title: Exploring Ground and Excited States via Single Reference Coupled-Cluster Theory and Algebraic Geometry
• Authors: Svala Sverrisdóttir, Fabian M. Faulstich,
• Abstract summary: This study provides insight into the intricate root structures of coupled cluster equations at both the CCD and CCSD level of theory. We compare the computed CC roots against various established theoretical upper bounds, shedding light on the accuracy and efficiency of these bounds. Our investigations reveal that for systems like lithium hydride, CC not only provides high-accuracy approximations to several excited state energies but also to the states themselves.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The exploration of the root structure of coupled cluster equations holds both foundational and practical significance for computational quantum chemistry. This study provides insight into the intricate root structures of these non-linear equations at both the CCD and CCSD level of theory. We utilize computational techniques from algebraic geometry, specifically the monodromy and parametric homotopy continuation methods, to calculate the full solution set. We compare the computed CC roots against various established theoretical upper bounds, shedding light on the accuracy and efficiency of these bounds. We hereby focus on the dissociation processes of four-electron systems such as (H$_2$)$_2$ in both D$_{2{\rm h}}$ and D$_{\infty {\rm h}}$ configurations, H$_4$ symmetrically distorted on a circle, and lithium hydride. We moreover investigate the ability of single-reference coupled cluster solutions to approximate excited state energies. We find that multiple CC roots describe energies of excited states with high accuracy. Our investigations reveal that for systems like lithium hydride, CC not only provides high-accuracy approximations to several excited state energies but also to the states themselves.

Related papers

• On the Coupled Cluster Doubles Truncation Variety of Four Electrons [0.0]
  We study the first genuinely nonlinear doubles regime of four electrons in the doubles approximation (CCD)<n>Using representation-theoretic arguments, we uncover a Pfaffian structure governing the quadratic relations that define the truncation variety for any $n$, and show that an exact tensor product factorization holds in a distinguished limit of disconnected doubles.
  arXiv  Detail & Related papers  (2026-02-18T16:28:24Z)
• Topological resolution of conical intersection seams and the coupled cluster bifurcation via mixed Hodge modules [0.0]
  Conical Intersections (CIs) is the central challenge of non-adiabatic quantum chemistry.<n>Standard Coupled Cluster (CC) theory suffers from root bifurcations near Ground State CIs.<n>We present textbfMorpheus, an open-source computational package that resolves these singularities.
  arXiv  Detail & Related papers  (2025-12-23T14:58:23Z)
• Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory [0.0]
  We study methods for efficient preparation of approximate ground states of $SU(3)$ lattice gauge theory on quantum hardware.<n>We develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices.
  arXiv  Detail & Related papers  (2025-09-30T07:01:26Z)
• Quantum Bootstrap Approach to a Non-Relativistic Potential for Quarkonium systems [1.0214800410255813]
  We use a non-relativistic potential approximation to determine the bound-state spectrum of Quarkonium systems.<n>This result provides theoretical support for the interpretation of this experimental phenomenon as the formation of a quasi-bound toponium state.
  arXiv  Detail & Related papers  (2025-08-04T21:40:10Z)
• Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases [0.0]
  This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models. We focus on transitioning these states from the conventional computational (sigmaz) basis to more complex bases, such as (phi, fracpi2, alpha) We present a novel algorithm that not only simplifies the basis transformation but also reduces computational complexity.
  arXiv  Detail & Related papers  (2024-03-05T19:43:33Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Bardeen-Cooper-Schrieffer interaction as an infinite-range Penson-Kolb pairing mechanism [0.0]
  We show that the well-known $(kuparrow, -kdownarrow)$ Bardeen-Cooper-Schrieffer interaction, when considered in real space, is equivalent to an infinite-range Penson-Kolb pairing mechanism. We investigate the dynamics of fermionic particles confined in a ring-shaped lattice.
  arXiv  Detail & Related papers  (2024-01-30T10:29:46Z)
• Many-Body Excited States with a Contracted Quantum Eigensolver [0.0]
  We develop an excited state approach based on the contracted quantum eigensolver (ES-CQE) We show the ES-CQE near-exact accuracy across the majority of states, covering regions of strong and weak electron correlation.
  arXiv  Detail & Related papers  (2023-05-16T17:53:07Z)
• Towards the simulation of transition-metal oxides of the cathode battery materials using VQE methods [0.0]
  Variational quantum eigensolver (VQE) is a hybrid quantum-classical technique that leverages noisy intermediate scale quantum hardware to obtain minimum eigenvalue of a model Hamiltonian. In this work, we employ VQE methods to obtain the ground-state energy of LiCoO$$, a candidate transition metal oxide used for battery cathodes.
  arXiv  Detail & Related papers  (2022-08-16T22:30:54Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids [58.720142291102135]
  We advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids. We also uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL)
  arXiv  Detail & Related papers  (2021-10-12T18:00:00Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• A multiconfigurational study of the negatively charged nitrogen-vacancy center in diamond [55.58269472099399]
  Deep defects in wide band gap semiconductors have emerged as leading qubit candidates for realizing quantum sensing and information applications. Here we show that unlike single-particle treatments, the multiconfigurational quantum chemistry methods, traditionally reserved for atoms/molecules, accurately describe the many-body characteristics of the electronic states of these defect centers.
  arXiv  Detail & Related papers  (2020-08-24T01:49:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.