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Scientific Reports

An anomaly in quantum phases induced by borders

Jun Jing, Mike Guidry, Lian-Ao Wu

Published Apr 24, 2020• 3 citations
Publisher

Abstract

The stationary behavior of a quantum system is determined by its Hamiltonian and its boundary conditions. All quantum phase transitions (QPT) reported previously were induced by changing the Hamiltonian. In a circular spin model with Heisenberg XY interactions and no magnetic field, we observe an anomaly in quantum phases caused by a qualitative change of the boundary condition. The unexpected anomaly features an infinite number of single-particle levels, in the same pattern as the single-photon-triggered quantum phase transition in the Rabi model.

DOI
10.1038/s41598-020-63555-x

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The stationary behavior of a quantum system is determined by its Hamiltonian and its boundary conditions. All quantum phase transitions (QPT) reported previously were induced by changing the Hamiltonian. In a circular spin model with Heisenberg XY interactions and no magnetic field, we observe an anomaly in quantum phases caused by a qualitative change of the boundary condition. The unexpected anomaly features an infinite number of single-particle levels, in the same pattern as the single-photon-triggered quantum phase transition in the Rabi model.
Quantum phase transitions, being in charge of the property of matter, are normally induced by varying the Hamiltonian and are characterized by an avoided level crossing between the ground and an excited state. Recently, a quantum phase anomaly induced by a boundary is predicted theoretically as the number of sites NNN goes to infinity in a one-dimensional Heisenberg spin XYXYXY model without an external magnetic field. The infinite-size lattice apparently is inaccessible in experiment, which prevents the experimental observation of the theoretical prediction. In this paper, we find that the finite-size odd-sited lattice can also give the infinite-size lattice's ground-state behavior, and successfully observe such a critical anomaly between two phases having topologically different boundary conditions for the Mott insulator in a finite-size photonic lattice.
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition between quantum fluctuations and mutual interactions among constituents of the system, not by thermal fluctuations; hence they can occur even at zero temperature. Examples of quantum phase transitions in many-body physics may be found in systems ranging from high-temperature superconductors to topological insulators. A quantum phase transition usually can be characterized by nonanalyticity/discontinuity in certain order parameters or divergence of the ground state energy eigenvalue and/or its derivatives with respect to certain physical quantities. Here in a circular one-dimensional spin model with Heisenberg XY interaction and no magnetic field, we observe critical phenomena for the n0=1/N→0n_0=1/N\rightarrow0n0​=1/N→0 Mott insulator caused by a qualitative change of the boundary condition. We demonstrate in the vicinity of the transition point a sudden change in ground-state properties accompanied by an avoided level-crossing between the ground and the first excited states. Notably, our result links conventional quantum phase transitions to microscopic boundary conditions, with significant implications for quantum information, quantum control, and quantum computing.
The ground state of a one-dimensional spin-1/2 chain with periodical boundary condition in the Heisenberg XY model is investigated. We consider the spatial correlation and concurrence between any nearest-neighbor pair of spins under the conditions of different coupling strength, anisotropic parameter and magnitude of a transverse field. Quantum phase transitions due to the competition between coupling and alignment which cause the abrupt changes of the correlation and concurrence are observed. The transition are direct results of the level crossing.
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system undergoes a qualitative change in the ground state when a control parameter in its Hamiltonian is varied. Here we report the first experimental study using the geometric phase as a topological test of quantum transitions of the ground state in a Heisenberg XY spin model. Using NMR interferometry, we measure the geometric phase for different adiabatic circuits that do not pass through points of degeneracy.
A quantum phase transition (QPT) in Hermitian systems is independent of the boundary condition in the thermodynamic limit. However, it may happen for a non-Hermitian system, that the QPT strongly depends on the boundary condition. We investigate the many-body ground-state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We employ a semilocalization state to describe a quantum phase that is a crossover from extended to localized state. The peculiar feature is that the decay length is of the order of the system size rather than fixed as a usual localized state. In addition, the spectral statistics is nonanalytic as asymmetrical hopping strengths vary, resulting a sudden charge of the ground state. The distinguishing feature of such a QPT is that the density of the ground-state energy varies smoothly due to unbroken symmetry. However, there are other observables, such as the ground-state center of mass and average current, which exhibit the behavior of second-order QPT. This behavior stems from time-reversal symmetry breaking of a macroscopic number of single-particle eigenstates.
Spin–phonon interaction effects in a spin-1/2 antiferromagnetic Heisenberg chain coupled to phonons are investigated in systems with variable crystal structures. By performing a unitary transformation to a Hamiltonian of the system, we derive effective Hamiltonians expanded in powers of spin–phonon and spin–spin couplings. Ground-state phase transitions between a spin-liquid phase and a spin-gapped phase are investigated by a level spectroscopy analysis of numerical diagonalization data of effective systems. Our results depend on whether the ground state of the Heisenberg chain is in the spin-liquid phase or the spin-gapped phase. In the system where the ground state is in the spin-liquid phase, the spin–phonon interaction causes the usual phase transition to the spin-gapped phase. On the other hand, in the system where the ground state is in the spin-gapped phase, the spin–phonon interaction causes the novel phase transition to the spin-liquid phase for some geometrical structures. The phase transition from the spin-gapped phase to the spin-liquid phase is observed by changing a parameter to control the change in a geometrical structure.