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Serwatka T, Roy PN. Ground states of planar dipolar rotor chains with recurrent neural networks. J Chem Phys 2024; 160:224103. [PMID: 38856054 DOI: 10.1063/5.0205466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2024] [Accepted: 05/27/2024] [Indexed: 06/11/2024] Open
Abstract
In this contribution, we employ a recurrent neural network (RNN) architecture in a variational optimization to obtain the ground state of linear chains of planar, dipolar rotors. We test different local basis sets and discuss their impact on the sign structure of the many-body ground state wavefunction. It is demonstrated that the RNN ansatz we employ is able to treat systems with and without a sign problem in the ground state. For larger chains with up to 50 rotors, accurate properties, such as correlation functions and Binder parameters, are calculated. By employing quantum annealing, we show that precise entanglement properties can be obtained. All these properties allow one to identify a quantum phase transition between a paraelectric and a ferroelectric quantum phase.
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Affiliation(s)
- Tobias Serwatka
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Orr L, Roy PN. Operator Formulation of Feynman Path Centroid Dynamics for Rotations. J Phys Chem A 2024; 128:3419-3433. [PMID: 38651978 DOI: 10.1021/acs.jpca.3c08201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
An operator formulation of centroid molecular dynamics (CMD) for rotational degrees of freedom is presented. The quasi-density operator concept was introduced by Jang and Voth [J. Chem. Phys 111, 2357 (1999)] and is used to obtain a phase-space mapping without the need for discretized path integrals. The approach allows the calculation of approximate Kubo-transformed time correlation functions. The particle on a ring is chosen as an illustrative example. Numerical results demonstrate that the proposed approach leads to accurate results when compared with exact diagonalization calculations for linear operators. At very low temperatures, it is found that rotational CMD yields results that are in exact agreement with the quantum dynamics of a spin-1 system.
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Affiliation(s)
- Lindsay Orr
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Serwatka T, Roy PN. Quantum criticality in chains of planar rotors with dipolar interactions. J Chem Phys 2024; 160:104302. [PMID: 38465677 DOI: 10.1063/5.0195453] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Accepted: 02/22/2024] [Indexed: 03/12/2024] Open
Abstract
In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.
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Affiliation(s)
- Tobias Serwatka
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Abalmasov VA, Vugmeister BE. Metastable states in the J_{1}-J_{2} Ising model. Phys Rev E 2023; 107:034124. [PMID: 37072970 DOI: 10.1103/physreve.107.034124] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 02/23/2023] [Indexed: 04/20/2023]
Abstract
We study the J_{1}-J_{2} Ising model on the square lattice using the random local field approximation (RLFA) and Monte Carlo (MC) simulations for various values of the ratio p=J_{2}/|J_{1}| with antiferromagnetic coupling J_{2}, ensuring spin frustration. RLFA predicts metastable states with zero order parameter (polarization) at low temperature for p∈(0,1). This is supported by our MC simulations, in which the system relaxes into metastable states with not only zero, but also with arbitrary polarization, depending on its initial value, external field, and temperature. We support our findings by calculating the energy barriers of these states at the level of individual spin flips relevant to the MC calculation. We discuss experimental conditions and compounds appropriate for experimental verification of our predictions.
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Affiliation(s)
- V A Abalmasov
- Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia
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Serwatka T, Melko RG, Burkov A, Roy PN. Quantum Phase Transition in the One-Dimensional Water Chain. PHYSICAL REVIEW LETTERS 2023; 130:026201. [PMID: 36706406 DOI: 10.1103/physrevlett.130.026201] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 11/08/2022] [Indexed: 06/18/2023]
Abstract
The concept of quantum phase transitions (QPTs) plays a central role in the description of condensed matter systems. In this Letter, we perform high-quality wave-function-based simulations to demonstrate the existence of a quantum phase transition in a crucially relevant molecular system, namely, water, forming linear chains of rotating molecules. We determine various critical exponents and reveal the water chain QPT to belong to the (1+1)-dimensional Ising universality class. Furthermore, the effect of breaking symmetries is examined, and it is shown that, by breaking the inversion symmetry, the ground state degeneracy of the ordered quantum phase is lifted to yield two many-body states with opposite polarization. The possibility of forming ferroelectric phases together with a thermal stability of the quantum critical regime up to ∼10 K makes the linear water chain a promising candidate as a platform for quantum devices.
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Affiliation(s)
- T Serwatka
- Department of Chemistry, University of Waterloo, Ontario N2L 3G1, Canada
| | - R G Melko
- Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - A Burkov
- Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - P-N Roy
- Department of Chemistry, University of Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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Serwatka T, Roy PN. Ferroelectric water chains in carbon nanotubes: Creation and manipulation of ordered quantum phases. J Chem Phys 2022; 157:234301. [PMID: 36550052 DOI: 10.1063/5.0131149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
Systems composed of molecular rotors are promising candidates as quantum devices. In this work, we employ our recently developed density matrix renormalization group approach to study such a rotor system, namely, linear chains of rotating para-water molecules encapsulated in a (6,5)-carbon nanotube. We show that the anisotropic environment provided by the nanotube breaks the inversion symmetry of the chain. This symmetry breaking lifts the degeneracy of the ground state and leads to a splitting between the left- and right-polarized states. In turn, a ferroelectric phase in nanoscopic systems is created, with a polarization that can be switched in a manner analogous to that of a supramolecular qubit. We present results for a few low-lying states and discuss the effect of external electric fields on the energy splitting and the occurrence of a quantum phase transition.
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Affiliation(s)
- Tobias Serwatka
- Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
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Morcillo-Arencibia MF, Alcaraz-Pelegrina JM, Sarsa AJ, Randazzo JM. An off-center endohedrally confined hydrogen molecule. Phys Chem Chem Phys 2022; 24:22971-22977. [PMID: 36125249 DOI: 10.1039/d2cp03456e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this study, we address the problem of a C60 endohedrally confined hydrogen molecule through a configuration-interaction approach to electronic dynamics. Modeling the confinement by means of a combination of two Woods-Saxon potentials, we analyze the stability of the system as a function of the nuclei position through the behavior of the electronic spectrum. After studying the convergence of two different partial wave expansions, one related to the molecular Coulomb centers and the other related to the off-centering of the C60 well, we found that the second approach provides a more accurate description of the system. Furthermore, we observed that the inter-atomic distance changes based on the position of the atoms inside the cavity. Thus, to obtain the most favourable energetic configuration for the molecule, it should be positioned inside the cavity next to the structure, where its size decreases.
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Affiliation(s)
- Milagros F Morcillo-Arencibia
- Departamento de Física, Campus de Rabanales, Edif. C2. Universidad de Córdoba, E-14071 Córdoba, Spain. .,Centro Atómico Bariloche, CNEA and CONICET, S. C. de Bariloche, Río Negro, Argentina
| | | | - Antonio J Sarsa
- Departamento de Física, Campus de Rabanales, Edif. C2. Universidad de Córdoba, E-14071 Córdoba, Spain.
| | - Juan M Randazzo
- Centro Atómico Bariloche, CNEA and CONICET, S. C. de Bariloche, Río Negro, Argentina
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