Related papers: Topological Order at Non-zero Temperature
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
This dissertation discusses some properties of topologically ordered states as they appear in the setting of infinite quantum spin systems. We begin by studying the set of infinite volume ground states for Kitaev's abelian quantum double…
We calculate exactly the von Neumann and topological entropies of the toric code as a function of system size and temperature. We do so for systems with infinite energy scale separation between magnetic and electric excitations, so that the…
Are systems that display Topological Quantum Order (TQO), and have a gap to excitations, hardware fault-tolerant at finite temperatures? We show that in surface code models that display low d-dimensional Gauge-Like Symmetries, such as…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum…
We consider two co-moving atoms on a stationary trajectory and develop a formalism to characterize the properties of such atoms. We give a criterion under which quantum coherence (QC) is frozen to a nonzero value and show that the frozen…
The integration of topological concepts into electronic energy band theory has been a transformative development in condensed matter physics. Since then, this paradigm has broadened its reach, extending to a variety of physical systems,…
We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order. We apply this measure to the toric code and two fractional quantum Hall models. We…
Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature…
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…
The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent…
We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such…
We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature~(Ostilli and Presilla 2021 \textit{J.…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
In the last two decades, a vast variety of topological phases have been described, predicted, classified, proposed, and measured. While there is a certain unity in method and philosophy, the phenomenology differs wildly. This work deals…
We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and…
We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The guiding principle behind our approach is that of symmetries and entanglement. We introduce the concept of low-dimensional…
We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The…