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arXiv:1909.02046 · Physical Review Research

Quasiparticles as detector of topological quantum phase transitions

Sourav Manna, N. S. Srivatsa, Julia Wildeboer, Anne E. B. Nielsen

Published Dec 31, 2020• 16 citations
arXivHTMLPDF

Abstract

A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems.They apply under different conditions, but do not cover the full range of many-body models.It is hence desirable to further expand the toolbox.Here, we propose to use quasiparticle properties to detect quantum phase transitions.The approach is independent from the choice of boundary conditions, and it does not assume a particular lattice structure.The probe is hence suitable for, e.g., fractals and quasicrystals.The method requires that one can reliably create quasiparticles in the considered systems.In the simplest cases, this can be done by a pinning potential, while it is less straightforward in more complicated systems.We apply the method to several rather different examples, including one that cannot be handled by the commonly used probes, and in all the cases we find that the numerical costs are low.This is so, because a simple property, such as the charge of the anyons, is sufficient to detect the phase transition point.For some of the examples, this allows us to study larger systems and/or further parameter values compared to previous studies.

DOI
10.1103/physrevresearch.2.043443

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A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems.They apply under different conditions, but do not cover the full range of many-body models.It is hence desirable to further expand the toolbox.Here, we propose to use quasiparticle properties to detect quantum phase transitions.The approach is independent from the choice of boundary conditions, and it does not assume a particular lattice structure.The probe is hence suitable for, e.g., fractals and quasicrystals.The method requires that one can reliably create quasiparticles in the considered systems.In the simplest cases, this can be done by a pinning potential, while it is less straightforward in more complicated systems.We apply the method to several rather different examples, including one that cannot be handled by the commonly used probes, and in all the cases we find that the numerical costs are low.This is so, because a simple property, such as the charge of the anyons, is sufficient to detect the phase transition point.For some of the examples, this allows us to study larger systems and/or further parameter values compared to previous studies.
Topological Quantum Field Theory or TQFT is a quantum field theory that calculates topological invariance in measurement theory and mathematical physics. In recent years, several attempts have been made to find efficient observations to determine the TQFT of quasiparticle properties. In this paper, we propose a different and very effective way to detect the critical points of TQFT by considering the system functions. We suggest the C-Function as a novel probe that is accurate for detecting the location of critical points on topological quantum. The C-function uses a holographic model to show a topological quantum phase transition between a simple topological isolation phase and a gapless Weyl semimetal. The quantum tipping point displays a strong Lifshitz-like anisotropy in the spatial direction, and a quantum phase transition that does not follow the standard Landau paradigm. The C-function precisely shows the global features of quantum criticality and distinguishes very accurately between two separate zero-temperature phases. Considering the C-function relationship with entanglement entropy can detect quantum phase transitions and can be applied outside the holographic framework. Keywords: quantum topologic, phase transitions, c-function
Opportunities for topological phase transitions in strongly correlated Fermi systems near a quantum critical point are explored as an alternative to collective scenarios for experimentally observed departures from standard Fermi-liquid behavior. Attention is focused on a quantum critical point at which the effective mass is divergent due to vanishing of the quasiparticle group velocity at the Fermi surface. Working within the original Landau quasiparticle theory, it is demonstrated that the quasiparticle picture can remain meaningful beyond the quantum critical point through rearrangements of the unstable normal Fermi surface and quasiparticle spectrum. Two possibilities emerge at zero temperature, depending on whether the quasiparticle interaction is regular or singular at zero momentum transfer. In the regular case, one type of topological phase transformation leads to a state with a multiconnected Fermi surface. In the singular case, another type of topological phase transition leads to an exceptional state containing a fermion condensate – the Fermi surface swells into a volume in momentum space, within which partial occupation prevails and quasiparticle energies are pinned to the chemical potential. As the temperature increases from zero to a characteristic value Tm, a crossover can occur from the state with multiple Fermi surfaces to that containing a fermion condensate.
In quantum many-body systems, characterizing topological phase transitions typically requires complex many-body topological invariants, which are costly to compute and measure. Inspired by quantum reservoir computing, we propose an unsupervised quantum phase detection method based on a many-body localized evolution, enabling efficient identification of phase transitions in the extended SSH model. The evolved quantum states produce feature distributions under local measurements, which, after simple post-processing and dimensionality reduction, naturally cluster according to different Hamiltonian parameters. Numerical simulations show that the evolution combined with local measurements can significantly amplify distinctions between quantum states, providing an efficient means to detect topological phase transitions. Our approach requires neither complex measurements nor full density matrix reconstruction, making it practical and feasible for noisy intermediate-scale quantum devices.
Quantum many-body systems undergoing phase transitions have been proposed as probes enabling beyond-classical enhancement of sensing precision. However, this enhancement is usually limited to a very narrow region around the critical point. Here, we systematically develop a modular approach for introducing multiple phase transitions in a many-body system. This naturally allows us to enlarge the region of quantum-enhanced precision by encompassing the newly created phase boundaries. Our approach is general and can be applied to both symmetry-breaking and topological quantum sensors. In symmetry-breaking sensors, we show that the newly created critical points inherit the original universality class and a simple total magnetization measurement already suffices to locate them. In topological sensors, our modular construction creates multiple bands which leads to a rich phase diagram. In both cases, Heisenberg scaling for Hamiltonian parameter estimation is achieved at all the phase boundaries. This can be exploited to create a global sensor which significantly outperforms a uniform probe.
Topological phases - systems with a global ordering in the entanglement - exhibit exotic excitations known as anyons which can display highly nontrivial (non-Abelian) statistics. Through transitions between such phases, these anyons can undergo rather surprising changes. Perhaps most surprisingly, one anyon can split into two or more anyons, some of which might condense or become confined. The authors propose here a complete set of order parameters which allow one to extract the full information about how the properties of anyons change through phase transitions, and to apply them to a range of topological phase transitions.
The macroscopic theory of anyon condensation, rooted in the categorical structure of topological excitations, provides a complete classification of gapped boundaries in topologically ordered systems, where distinct boundaries correspond to the condensation of different Lagrangian algebras. However, an intrinsic and direct understanding of anyon condensation in lattice models, grounded in the framework of Lagrangian algebras, remains undeveloped. In this paper, we propose a systematic framework for constructing all gapped boundaries of Kitaev's quantum double models directly from the data of Lagrangian algebras. Central to our approach is the observation that bulk interactions in the quantum double models admit two complementary interpretations: the anyon-creating picture and the anyon-probing picture. Generalizing this insight to the boundary, we derive the consistency condition for boundary ribbon operators that respect the mathematical axiomatic structure of Lagrangian algebras. Solving these conditions yields explicit expressions for the local boundary interactions required to realize gapped boundaries. We also provide three families of solutions that cover a broad range of cases. Our construction provides a microscopic characterization of the bulk-to-boundary anyon condensation dynamics via the action of ribbon operators. Moreover, all these boundary terms are supported within a common effective Hilbert space, making further studies on pure boundary phase transitions natural and convenient. Given the broad applicability of anyon condensation theory, we believe that our approach can be generalized to planar topological codes, extended string-net models, or higher-dimensional topologically ordered systems.