Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Frustration of being Odd: Resilience of the Topological Phases
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the magnetic order that characterizes such models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the frustrated boundary conditions on several models supporting topological orders. In particular, we focus on the Cluster-Ising model, which presents a symmetry protected topologically ordered phase, and the Kitaev and AKLT chains that, on the contrary, are characterized by a purely topological order. In all these models we find that the different topological orders are not affected by the frustrated boundary conditions. This observation leads naturally to the conjecture that systems supporting topological order are resilient to topological frustration, and thus that topological phases could be identified through this resilience.
rate research
Read More
A central tenant in the classification of phases is that boundary conditions cannot affect the bulk properties of a system. In this work, we show striking, yet puzzling, evidence of a clear violation of this assumption. We use the prototypical example of an XYZ chain with no external field in a ring geometry with an odd number of sites and both ferromagnetic and antiferromagnetic interactions. In such a setting, even at finite sizes, we are able to calculate directly the spontaneous magnetizations that are traditionally used as order parameters to characterize the systems phases. When ferromagnetic interactions dominate, we recover magnetizations that in the thermodynamic limit lose any knowledge about the boundary conditions and are in complete agreement with standard expectations. On the contrary, when the system is governed by antiferromagnetic interactions, the magnetizations decay algebraically to zero with the system size and are not staggered, despite the AFM coupling. We term this behavior {it ferromagnetic mesoscopic magnetization}. Hence, in the antiferromagnetic regime, our results show an unexpected dependence of a local, one--spin expectation values on the boundary conditions, which is in contrast with predictions from the general theory.
It has been recently proven that new types of bulk, local order can ensue due to frustrated boundary condition, that is, periodic boundary conditions with an odd number of lattice sites and anti-ferromagnetic interactions. For the quantum XY chain in zero external fields, the usual antiferromagnetic order has been found to be replaced either by a mesoscopic ferromagnet or by an incommensurate AFM order. In this work we examine the resilience of these new types of orders against a defect that breaks the translational symmetry of the model. We find that, while a ferromagnetic defect restores the traditional, staggered order, an AFM one stabilizes the incommensurate order. The robustness of the frustrated order to certain kinds of defects paves the way for its experimental observability.
Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a systems phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.
At the core of every frustrated system, one can identify the existence of frustrated rings that are usually interpreted in terms of single--particle physics. We check this point of view through a careful analysis of the entanglement entropy of both models that admit an exact single--particle decomposition of their Hilbert space due to integrability and those for which the latter is supposed to hold only as a low energy approximation. In particular, we study generic spin chains made by an odd number of sites with short-range antiferromagnetic interactions and periodic boundary conditions, thus characterized by a weak, i.e. nonextensive, frustration. While for distances of the order of the correlation length the phenomenology of these chains is similar to that of the non-frustrated cases, we find that correlation functions involving a number of sites scaling like the system size follow different rules. We quantify the long-range correlations through the von Neumann entanglement entropy, finding that indeed it violates the area law, while not diverging with the system size. This behavior is well fitted by a universal law that we derive from the conjectured single--particle picture.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
