arXiv:1811.11115

Order Fractionalization

Yashar Komijani, Anna I. Tóth, Premala Chandra, Piers Coleman

Published Nov 27, 2018• 2 citations

Abstract

The confluence of quantum mechanics and complexity, which leads to the emergence of rich, exotic states of matter, motivates the extension of our concepts of quantum ordering. The twin concepts of spontaneously broken symmetry, described in terms of a Landau order parameter, and of off-diagonal long-range order (ODLRO), are fundamental to our understanding of phases of matter. In electronic matter it has long been assumed that Landau order parameters involve an even number of electron fields, with integer spin and even charge, that are bosons. On the other hand, in low-dimensional magnetism, operators are known to fractionalize so that the excitations carry spin-1/2. Motivated by experiment, mean-field theory and computational results, we extend the concept of ODLRO into the time domain, proposing that in a broken symmetry state, quantum operators can fractionalize into half-integer order parameters. Using numerical renormalization group studies we show how such fractionalized order can be induced in quantum impurity models. We then conjecture that such order develops spontaneously in lattice quantum systems, due to positive feedback, leading to a new family of phases, manifested by a coincidence of broken symmetry and fractionalized excitations that can be detected by experiment.

DOI: 10.48550/arxiv.1811.11115

Related papers

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

Григорий Ефимович Воловик

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ Q of the charge Q and the energy relaxation time τ E . If τ Q ≫ τ E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid 4He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.

arXiv:1309.1845Journal of Experimental and Theoretical Physics LettersDec 1, 201342 citations

Experimental identification of quantum spin liquids

Jinsheng Wen, Shun-Li Yu, Shiyan Li +2 more

Abstract In condensed matter physics there is a novel phase termed ‘quantum spin liquid’, in which strong quantum fluctuations prevent long-range magnetic order from being estab lished, and so electron spins do not form an ordered pattern but remain liquid-like even at absolute zero temperature. Such a phase is not involved in any spontaneous symmetry breaking and local order parameter, and to understand it is beyond conventional phase transition theory. Due to the rich physics and exotic properties of quantum spin liquids, such as long-range entanglement and fractional quantum excitations, which are believed to hold great potential for quantum communication and computation, they have been intensively studied since the concept was proposed in 1973 by P.W. Anderson. Currently, experimental identification of a quantum spin liquid remains a great challenge. Here, we highlight some interesting experimental progress that has been made recently. We also discuss outstanding issues and raise questions that we consider to be important for future research.

arXiv:1904.04435npj Quantum MaterialsApr 5, 2019245 citations

Transport and Symmetry Breaking in Strongly Correlated Systems With Topological Order

Shubhayu Chatterjee

This thesis is devoted to the study of strongly correlated phases of quantum matter in two spatial dimensions. In presence of strong interactions, the electron can split up into separate spin and charge degrees of freedom. The diagnosis of such fractionalized excitations in recent experiments, as well as finding new probes for their detection, comprise the two major themes of this thesis.\nThe first part of the thesis, comprising chapters 2-6, discusses the relevance of fractionalization to the pseudogap phase of the underdoped high Tc cuprate superconductors. This is motivated by transport experiments that show a violation of Luttinger's theorem, possible only in the presence of topological order that can arise naturally as a consequence of fractionalization. Chapters 2 and 3 focus on phenomenological models with bosonic charge carriers and fermionic spin carriers, and investigate transport properties as well as various confinement transitions to symmetry broken phases. Chapters 4, 5 and 6 deal with a different framework of electron fractionalization, where the charge carriers are fermionic and spin carriers are bosonic. We find that these models can better explain the thermal and electrical transport properties in chapter 5. In chapters 6 and 7, we show how such models arise naturally from quantum fluctuations of antiferromagnetism, and can simultaneously intertwine the anti-nodal spectral gap with the discrete broken symmetries that are observed in the cuprates. \nThe second part of the thesis, comprising chapters 7 and 8, proposes new experimental probes to study the behavior of insulating two dimensional quantum magnets. Aided by geometric frustration and strong quantum fluctuations, they may realize a spin liquid ground state which can be extremely difficult to detect via conventional probes. Chapter 7 discusses how novel spin-transport probes from the spintronics community can be used to detect fractionalized excitations in a quantum spin liquid. Chapter 8 studies how the temperature dependent anisotropy of in-plane versus out-of-plane thermal conductivities can serve as an explicit signature of fractionalization in layered two-dimensional materials.

May 11, 20180 citations

Detecting hidden order in fractional Chern insulators

Fabian J. Pauw, Felix A. Palm, Ulrich Schollwöck +3 more

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of nonlocal order parameters, which require measurements on extensively many particles simultaneously—an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for experimental confirmation of nonlocal topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the ν=1/2 -Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent 1/ν=2 , and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of nonlocal topological orders, e.g., in topological states with non-Abelian anyonic excitations. Published by the American Physical Society 2024

arXiv:2309.03666Physical Review ResearchMay 17, 20245 citations

Continuous order-to-order quantum phase transitions from fixed-point annihilation

David Jonas Moser, Lukas Janssen

Abstract A central concept in the theory of phase transitions beyond the Landau–Ginzburg–Wilson paradigm is fractionalization: the formation of new quasiparticles that interact via emergent gauge fields. This concept has been extensively explored in the context of continuous quantum phase transitions between distinct orders that break different symmetries. We propose a mechanism for continuous order-to-order quantum phase transitions that operates independently of fractionalization. This mechanism is based on the collision and annihilation of two renormalization group fixed points: a quantum critical fixed point and an infrared stable fixed point. The annihilation of these fixed points rearranges the flow topology, eliminating the disordered phase associated with the infrared stable fixed point and promoting a second critical fixed point, unaffected by the collision, to a quantum critical point between distinct orders. We argue that this mechanism is relevant to a broad spectrum of physical systems. In particular, it can manifest in Luttinger fermion systems in three spatial dimensions, leading to a continuous quantum phase transition between an antiferromagnetic Weyl semimetal state, which breaks time-reversal symmetry, and a nematic topological insulator, characterized by broken lattice rotational symmetry. This continuous antiferromagnetic-Weyl-to-nematic-insulator transition might be observed in rare-earth pyrochlore iridates R 2 Ir2O7. Other possible realizations include kagome quantum magnets, quantum impurity models, and quantum chromodynamics with supplemental four-fermion interactions.

arXiv:2412.06890Reports on Progress in PhysicsSep 1, 20252 citations

Fractionalization and disorder in strongly correlated systems

Shackleton, Henry Joseph

Emergence in systems of many electrons can lead to macroscopic demonstrations of quantum mechanics which are intrinsically many-body. A primary focus of this dissertation is the phenomena of fractionalization, where the effective quasiparticles which emerge at long distances exhibit fractional quantum numbers of the microscopic degrees of freedom. The interplay between these emergent degrees of freedom and the microscopic symmetries can lead to a number of exotic properties including competing orders and unconventional phase transitions. I explore this phenomena in a number of platforms. This includes quantum antiferromagnets which can give rise to \textit{quantum spin liquids}, where we predict critical properties of phase transitions between spin liquids and conventionally-ordered phases - due to the fractionalized excitations, such critical theories deviate from traditional Landau-Ginzburg predictions. I also study the interplay between fractionalized spin and charge excitations, as well as fractionalization in non-equilibrium contexts. The second goal of this dissertation is to investigate the properties of disordered, strongly interacting, zero dimensional systems which exemplify many notable properties of higher-dimensional systems, such as doping-induced quantum criticality and non-Fermi liquid transport. The effects of disorder play an essential role in these models, leading to phenomena such as spin glass phases and conductance fluctuations which we investigate through both numerical and analytical methods.

Jan 1, 20240 citations