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Physical Review A

Experimental demonstration of a quantum anomaly induced by borders

Yao Wang, Yong‐Heng Lu, Jun Gao, Lian-Ao Wu, Xian‐Min Jin

Published Aug 18, 2021• 1 citation
Publisher

Abstract

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 $N$ goes to infinity in a one-dimensional Heisenberg spin $XY$ 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.

DOI
10.1103/physreva.104.022419

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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.
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 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.
Abstract In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Here we show an example of the opposite. We consider a spin chain with two competing interactions, set on a ring with an odd number of sites. When only the dominant interaction is antiferromagnetic, and thus induces topological frustration, the standard antiferromagnetic order (expressed by the magnetization) is destroyed. When also the second interaction turns from ferro to antiferro, an antiferromagnetic order characterized by a site-dependent magnetization which varies in space with an incommensurate pattern, emerges. This modulation results from a ground state degeneracy, which allows to break the translational invariance. The transition between the two cases is signaled by a discontinuity in the first derivative of the ground state energy and represents a quantum phase transition induced by a special choice of boundary conditions.
We discuss the boundary critical behaviors of two-dimensional (2D) quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the one-dimensional boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: (i) the quantum phase transition between a 2D Z2{Z}_{2}Z2​ topological order and an ordered phase with spontaneous symmetry breaking; (ii) the continuous quantum phase transition between metal and a particular type of Mott insulator [U(1)\mathrm{U}(1)U(1) spin liquid]. In particular, we obtain the critical exponents and scaling laws of these exotic quantum phase transitions when the systems are probed from the boundary in proposed experimental setup. These critical exponents obtained are significantly different from those one would see through bulk measurements. This theoretical study could be relevant to many purely 2D systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.
Disordered quantum antiferromagnets in two-dimensional compounds have been a focus of interest in the last years due to their exotic properties. However, with very few exceptions, the ground states of the corresponding Hamiltonians are notoriously difficult to simulate making their characterization and detection very elusive, both theoretically and experimentally. Here we propose a method to signal quantum disordered antiferromagnets by doing exact diagonalization in small lattices using random boundary conditions and averaging the observables of interest over the different disorder realizations. We apply our method to study the Heisenberg spin-1/2 model in an anisotropic triangular lattice. In this model, the competition between frustration and quantum fluctuations might lead to some spin-liquid phases as predicted from different methods ranging from spin-wave mean-field theory to 2D-DMRG or PEPS. Our method accurately reproduces the ordered phases expected of the model and signals quantum disordered phases by the presence of a large number of quasidegenerate ground states together with an undefined local order parameter. The method presents a weak dependence on finite-size effects.
Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground-state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground-state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground-state fidelity per lattice site is universal, in the sense that it is model independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin-1/2 XYX model in an external magnetic field on an infinite-size lattice in one spatial dimension.