1
|
Kim J, Kim D, Kim DH. Neural-network quantum-state study of the long-range antiferromagnetic Ising chain. Phys Rev E 2024; 109:064123. [PMID: 39020874 DOI: 10.1103/physreve.109.064123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2023] [Accepted: 05/28/2024] [Indexed: 07/19/2024]
Abstract
We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions using the variational Monte Carlo method with the restricted Boltzmann machine employed as a trial wave function ansatz. First, we measure the critical exponents and the central charge through the finite-size scaling analysis, verifying the contrasting observations in the previous tensor network studies. The correlation function exponent and the central charge deviate from the short-range (SR) Ising values at a small decay exponent α_{LR}, while the other critical exponents examined are very close to the SR Ising exponents regardless of α_{LR} examined. However, in the further test of the critical Binder ratio, we find that the universal ratio of the SR limit does not hold for α_{LR}<2, implying a deviation in the criticality. On the other hand, we find evidence of the conformal invariance breakdown in the conformal field theory (CFT) test of the correlation function. The deviation from the CFT description becomes more pronounced as α_{LR} decreases, although a precise breakdown threshold is yet to be determined.
Collapse
|
2
|
Feng L, Katz O, Haack C, Maghrebi M, Gorshkov AV, Gong Z, Cetina M, Monroe C. Continuous symmetry breaking in a trapped-ion spin chain. Nature 2023; 623:713-717. [PMID: 37968402 DOI: 10.1038/s41586-023-06656-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 09/20/2023] [Indexed: 11/17/2023]
Abstract
One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions1. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter2,3. Our preparation relies on simultaneous control over an array of tightly focused individual addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.
Collapse
Affiliation(s)
- Lei Feng
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Or Katz
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
| | - Casey Haack
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Mohammad Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansings, MI, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA
| | - Zhexuan Gong
- Department of Physics, Colorado School of Mines, Golden, CO, USA
| | - Marko Cetina
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Christopher Monroe
- Duke Quantum Center, Department of Physics and Electrical and Computer Engineering, Duke University, Durham, NC, USA.
- IonQ, Inc., College Park, MD, USA.
| |
Collapse
|