Spin-Orbit Physics in the Mott Regime Leon Balents, KITP “Exotic Insulating State of Matter”, JHU, January 2010 Collaborator
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Mott Insulators Atomic Limit - View Electrons in Real Space
Mott insulators Atomic limit - view electrons in real space Virtual system: lattice of H-Atoms: aB << d 2aB d H Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer - H H + -t ionization energy H delocalization localization kinetic energy charge excitation energy metal Mott insulator Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer ionization energy H -t S = 1/2 Mott isolator effective low-energy model low-energy physics no charge fluctuation only spin fluctuation Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 „ground state“ t = 0 E charge excitation U h d Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 t > 0 „ground state“ E W = 4d t U charge excitation h d metal-insulator transition: Uc = 4dt Mott insulators Metal-insulator transition from the metallic side h d tight-binding model density empty sites h = 1/4 doubly occupied sites d = 1/4 half-filled singly occupied sites s = 1/2 conduction band reducing mobility Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side Gutzwiller-approach: variational diminish double-occupancy uncorrelated state variational groundstate density of doubly occupied sites renormalized hopping Mott insulators Gutzwiller approximation Metal-insulator -
Vortex-Matter in Multi-Component Superconductors
Vortex-matter in Multi-component Superconductors JOHAN CARLSTRÖM Licentiate thesis Stockholm, Sweden 2012 TRITA-FYS 2012:90 ISSN 0280-316X KTH Teoretisk fysik ISRN KTH/FYS/--12:90--SE AlbaNova universitetscentrum ISBN 978-91-7501-611-5 SE-106 91 Stockholm Sweden Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie licentiatexamen i teoretisk fysik den 14 Januari 2013 kl 10:00 i sal FA32, AlbaNova Universitetscentrum. c Johan Carlström, December 2012 Tryck: Universitetsservice US AB 3 Abstract The topic of this thesis is vortex-physics in multi component Ginzburg- Landau models. These models describe a newly discovered class of supercon- ductors with multiple superconducting gaps, and posses many properties that set them apart from single component models. The work presented here relies on large scale computer simulations using various numerical techniques, but also some analytical methods. In Paper I, Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors, we show that in multiband supercon- ductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vor- tices by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields, leading to phase separation into domains of two-component Meissner states and vortex droplets. In paper II, Type-1.5 superconductivity in multiband systems: Effects of interband couplings, we investigate the appearance of Type-1.5 superconduc- tivity in the case with two active bands and substantial inter-band couplings. -
9 Quantum Phases and Phase Transitions of Mott Insulators
9 Quantum Phases and Phase Transitions of Mott Insulators Subir Sachdev Department of Physics, Yale University, P.O. Box 208120, New Haven CT 06520-8120, USA, [email protected] Abstract. This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. Mott insulators in the simplest class have an even number of S =1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S =1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S =1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations. 9.1 Introduction The physics of Mott insulators in two and higher dimensions has enjoyed much attention since the discovery of cuprate superconductors. While a quan- titative synthesis of theory and experiment in the superconducting materials remains elusive, much progress has been made in describing a number of antiferromagnetic Mott insulators. -
Structural Superfluid-Mott Insulator Transition for a Bose Gas in Multi
Structural Superfluid-Mott Insulator Transition for a Bose Gas in Multi-Rods Omar Abel Rodríguez-López,1, ∗ M. A. Solís,1, y and J. Boronat2, z 1Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000 Ciudad de México, México 2Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, España (Dated: Modified: January 12, 2021/ Compiled: January 12, 2021) We report on a novel structural Superfluid-Mott Insulator (SF-MI) quantum phase transition for an interacting one-dimensional Bose gas within permeable multi-rod lattices, where the rod lengths are varied from zero to the lattice period length. We use the ab-initio diffusion Monte Carlo method to calculate the static structure factor, the insulation gap, and the Luttinger parameter, which we use to determine if the gas is a superfluid or a Mott insulator. For the Bose gas within a square Kronig-Penney (KP) potential, where barrier and well widths are equal, the SF-MI coexistence curve shows the same qualitative and quantitative behavior as that of a typical optical lattice with equal periodicity but slightly larger height. When we vary the width of the barriers from zero to the length of the potential period, keeping the height of the KP barriers, we observe a new way to induce the SF-MI phase transition. Our results are of significant interest, given the recent progress on the realization of optical lattices with a subwavelength structure that would facilitate their experimental observation. I. INTRODUCTION close experimental realization of a sequence of Dirac-δ functions, forming the well-known Dirac comb poten- Phase transitions are ubiquitous in condensed matter tial [13], and could be useful to test many mean-field physics. -
![Arxiv:2002.00554V2 [Cond-Mat.Str-El] 28 Jul 2020](https://docslib.b-cdn.net/cover/8297/arxiv-2002-00554v2-cond-mat-str-el-28-jul-2020-248297.webp)
Arxiv:2002.00554V2 [Cond-Mat.Str-El] 28 Jul 2020
Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices Zhihao Xu1, 2, 3, 4, ∗ and Shu Chen2, 5, 6, y 1Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China 2Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, P.R.China 4State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, P.R.China 5School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China 6Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by the strong repulsion results in a stable topological Bose-Mott insulator which has shares features similar to the Hermitian case. However, for the non-Hermitian model related to the one-body loss, we find the non-Hermitian topological Mott insulators are unstable with a finite imaginary excitation gap. Finally, we also discuss the stability of the Mott phase in the presence of two-body loss by solving the Lindblad master equation. -
Polariton Panorama (QED) with Atomic Systems
Nanophotonics 2020; ▪▪▪(▪▪▪): 20200449 Review D. N. Basov*, Ana Asenjo-Garcia, P. James Schuck, Xiaoyang Zhu and Angel Rubio Polariton panorama https://doi.org/10.1515/nanoph-2020-0449 (QED) with atomic systems. Here, we attempt to summarize Received August 5, 2020; accepted October 2, 2020; (in alphabetical order) some of the polaritonic nomenclature published online November 11, 2020 in the two subfields. We hope this summary will help readers to navigate through the vast literature in both of Abstract: In this brief review, we summarize and elaborate these fields [1–520]. Apart from its utilitarian role, this on some of the nomenclature of polaritonic phenomena summary presents a broad panorama of the physics and and systems as they appear in the literature on quantum technology of polaritons transcending the specifics of materials and quantum optics. Our summary includes at particular polaritonic platforms (Boxes 1 and 2). We invite least 70 different types of polaritonic light–matter dres- readers to consult with reviews covering many important sing effects. This summary also unravels a broad pano- aspects of the physics of polaritons in QMs [1–3], atomic and rama of the physics and applications of polaritons. A molecular systems [4], and in circuit QED [5, 6], as well as constantly updated version of this review is available at general reviews of the closely related topic of strong light– https://infrared.cni.columbia.edu. matter interaction [7–11, 394]. A constantly updated version Keywords: portions; quantum electrodynamics; quantum is available at https://infrared.cni.columbia.edu. materials; quantum optics. Anderson–Higgs polaritons [12, 13]. -
Theory of Nematic Fractional Quantum Hall State
Theory of Nematic Fractional Quantum Hall State Yizhi You,1 Gil Young Cho,1 and Eduardo Fradkin1, 2 1Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA 2Kavli Institute for Theoretical Physics, University of California Santa Barbara, CA 93106-4030, USA (Dated: July 9, 2018) We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall (FQH) states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has z = 2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the non-dissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic FQH fluid into a nematic fractional quantum Hall phase. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of Girvin-MacDonald-Platzman (GMP) mode collapses at the isotropic-nematic quantum phase transition. On the other hand, Laughlin quasiparticles and the Kohn collective mode remain gapped at this quantum phase transition, and Kohn’s theorem is satisfied. The leading couplings between the nematic order parameter and the gauge fields include a term of the same form as the Wen-Zee term. A disclination of the nematic order parameter carries an unquantized electric charge. We also discuss the relation between nematic degrees of freedom and the geometrical response of the fractional quantum Hall fluid. -
Mott Insulators
Quick and Dirty Introduction to Mott Insulators Branislav K. Nikoli ć Department of Physics and Astronomy, University of Delaware, U.S.A. PHYS 624: Introduction to Solid State Physics http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html Weakly correlated electron liquid: Coulomb interaction effects When local perturbation δ U ( r ) potential is switched on, some electrons will leave this region in order to ensure ε≃ µ constant F (chemical potential is a thermodynamic potential; therefore, in equilibrium it must be homogeneous throughout the crystal). δ= ε δ n()r eD ()F U () r δ≪ ε assume:e U (r ) F ε→ = θεε − f( , T 0) (F ) PHYS 624: Quick and Dirty Introduction to Mott Insulators Thomas –Fermi Screening Except in the immediate vicinity of the perturbation charge, assume thatδ U ( r ) is caused eδ n (r ) by the induced space charge → Poisson equation: ∇2δU(r ) = − ε − 0 1 ∂ ∂ αe r/ r TF ∇2 = r 2 ⇒ δ U (r ) = 2 −1/ 6 ∂ ∂ 2 rrr r 1 n 4πℏ ε ≃ = 0 rTF , a 0 ε 2 a3 me 2 r = 0 0 TF 2 ε = ⋅23− 3 Cu = e D (F ) nCu8.510 cm , r TF 0.55Å q in vacuum:D (ε )= 0, δ U (r ) = = α F πε 4 0 2 1/3 312n m 2/3ℏ 2/3− 4 1/3 n D()ε= =() 3,3 πεπ2 n = () 222 nr⇒ = () 3 π F ε π2ℏ 2 F TF π 2F 2 2 m a 0 PHYS 624: Quick and Dirty Introduction to Mott Insulators Mott Metal-Insulator Transition 1 a r2≃0 ≫ a 2 TF 4 n1/3 0 −1/3 ≫ n4 a 0 Below the critical electron concentration, the potential well of the screened field extends far enough for a bound state to be formed → screening length increases so that free electrons become localized → Mott Insulators Examples: transition metal oxides, glasses, amorphous semiconductors PHYS 624: Quick and Dirty Introduction to Mott Insulators Metal vs. -
Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene
Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Po, Hoi Chun et al. "Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene." Physical Review X 8, 3 (September 2018): 031089 As Published http://dx.doi.org/10.1103/PhysRevX.8.031089 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/118618 Terms of Use Creative Commons Attribution Detailed Terms http://creativecommons.org/licenses/by/3.0 PHYSICAL REVIEW X 8, 031089 (2018) Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene Hoi Chun Po,1 Liujun Zou,1,2 Ashvin Vishwanath,1 and T. Senthil2 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 4 June 2018; revised manuscript received 13 August 2018; published 28 September 2018) A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat miniband that arises a “magic” twist angle. However, the nature of the Mott insulator, the origin of superconductivity, and an effective low-energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks Uð1Þ valley symmetry and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hund’s coupling. We also identify symmetry-related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight- binding description. -
Graphene Reveals Its Strange Side
VIEWPOINT Graphene Reveals Its Strange Side Experiments on magic-angle graphene reveal a ``strange metal'' phase and transport behavior consistent with so-called Planckian dissipation. by Subir Sachdev∗ with a low-temperature transport behavior called Planckian dissipation [2, 3]. The same association is found by Jarillo- agic-angle graphene captured the attention of Herrero and colleagues in magic-angle graphene, providing condensed-matter physicists in 2018 when it further evidence that strange metals are united by a funda- was discovered that this material—made of two mentally new form of transport that theorists are busy trying sheets of graphene with slightly misaligned lat- to characterize. Mtice orientations (Fig. 1)—is a superconductor. Moreover, The transport of electrical and heat currents in metals was observations showed that the phase diagram of magic- once a well-understood corner of condensed-matter physics. angle graphene is similar to that of copper oxide high- This understanding was based on the Drude formula, which temperature superconductors, with an insulating region relates the electrical conductivity to the density of mobile next to a dome-shaped superconducting region (see Trend: electrons, the mass of an electron, and the time between Bilayer Graphene’s Wicked, Twisted Road). Now, Pablo scattering events, t. The original theory, developed by Paul Jarillo-Herrero from the Massachusetts Institute of Technol- Drude in 1900, treated the electrons as classical particles and ogy, Cambridge, and his colleagues report that magic-angle largely ignored electron-electron interactions. Remarkably, graphene has another remarkable feature of the cuprate Drude’s formula survived a quantum-mechanics update in phase diagram: a “strange metal” phase in which the re- the 1930s, in which the electron mass was replaced by sistivity scales linearly with temperature down to very low the effective mass of an electronic “quasiparticle,” and the temperatures [1]. -
Institute Lecture
Institute Lecture Quantum Mechanics Without Particles Professor Subir Sachdev Department of Physics, Harvard University . Tuesday, 21st January, 2014, Time: 6.00 PM, Venue: L-17, Lecture Hall Complex Abstract Quantum mechanics provides a thorough understanding of the physical properties of most common metals, insulators, and superconductors. Even 23 though we cannot solve the Schrödinger equation for 10 particles, we are able to make progress because the electrons move essentially independent of each other. However, in many modern materials, and particularly in the high temperature superconductors, there are important regimes where the independent-electron paradigm breaks down, and we have to deal with wave functions in which all the electrons are entangled with each other in a non- local manner. Understanding such quantum states, in which no particle-like excitations can be identified, is a major theoretical challenge. In this talk, we will describe recent progress in this field using quantum field theory, string theory, and computer simulations. These advances shed light on many of the puzzling features of phase diagrams of the high temperature superconductors. About the speaker Prof. Subir Sachdev is a distinguished condensed matter physicist. He is very well known for his research on quantum phase transitions, and its application to a variety of quantum materials, such as the high temperature superconductors. His book "Quantum Phase Transitions" (Cambridge University Press) has formed the basis of much subsequent research. More recently, he pioneered the application of string theory to the study of quantum phase transitions in condensed matter physics, such as the superfluid- insulator transition of bosons moving in a lattice. -
Adrian Del Maestro's CV.PDF
Adrian Del Maestro Department of Physics University of Vermont 82 University Place Burlington, VT 05405 USA Phone: 802-656-0068 Fax: 802-656-0817 Email: [email protected] URL: http://www.delmaestro.org/adrian/ Education Ph.D. in Physics, 2008. Thesis: The superconductor-metal quantum phase transition in ultra-narrow wires. Supervisor: Subir Sachdev. Harvard University, Cambridge, MA, USA M.S. in Physics, 2005 Yale University, New Haven, CT, USA M.Sc. in Physics, 2003. Thesis: Quantum spin fluctuations in the Heisenberg-like pyrochlore antiferromagnet gadolinium titanate. Supervisor: Michel Gingras. University of Waterloo, Waterloo, ON, Canada B.Sc. in Physics joint with Mathematics, 2002. Graduated summa cum laude. University of Waterloo, Waterloo, ON, Canada Professional Experience Assistant Professor of Physics University of Vermont (Burlington, VT, USA) 2011–Present Distinguished Postdoctoral Fellow Institute for Quantum Matter, Johns Hopkins University (Baltimore, MD, USA) 2010–2011 Postdoctoral Research Scientist University of British Columbia (Vancouver, BC, Canada) 2008 Research Scientist Harvard University (Cambridge, MA, USA) 2008– 2008 System Administrator Harvard University (Cambridge, MA, USA) 2006– 2008 Lab Technician University of Western Ontario, Brain Research Laboratories (London, ON, Canada) 1999 Publications (30 total, h-index: 15, citations: 597) 1. C. M. Herdman, P.-N. Roy, R.G. Melko and A. Del Maestro, Entanglement area law in superfluid 4He, Nature Phys. 4075, 1 (2017). 2. Adrian Del Maestro and Massimo Boninsegni, Absence of superfluidity in a quasi-one-dimensional parahydrogen fluid adsorbed inside carbon nanotubes, Phys. Rev. B 95, 054517 (2017). 3. C. M. Herdman, P.-N. Roy, R. G. Melko and A. Del Maestro, Spatial entanglement entropy in the ground state of the Lieb-Liniger model, Phys.