N ON - EQUILIBRIUM DYNAMIC CRITICAL SCALING OF THE QUANTUM I SING CHAIN Michael Kolodrubetz Princeton University In collaboration with: Bryan Clark, David.

Slides:

Advertisements

Similar presentations

APRIL 2010 AARHUS UNIVERSITY Simulation of probed quantum many body systems.

Advertisements

Unveiling the quantum critical point of an Ising chain Shiyan Li Fudan University Workshop on “Heavy Fermions and Quantum Phase Transitions” November 2012,

Theory of the pairbreaking superconductor-metal transition in nanowires Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

Dynamics of bosonic cold atoms in optical lattices. K. Sengupta Indian Association for the Cultivation of Science, Kolkata Collaborators: Anirban Dutta,

Prethermalization. Heavy ion collision Heavy ion collision.

Quantum Critical Behavior of Disordered Itinerant Ferromagnets D. Belitz – University of Oregon, USA T.R. Kirkpatrick – University of Maryland, USA M.T.

Dynamical mean-field theory and the NRG as the impurity solver Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.

D-wave superconductivity induced by short-range antiferromagnetic correlations in the Kondo lattice systems Guang-Ming Zhang Dept. of Physics, Tsinghua.

Non-equilibrium dynamics in the Dicke model Izabella Lovas Supervisor: Balázs Dóra Budapest University of Technology and Economics

Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,

Quantum phase transitions in anisotropic dipolar magnets In collaboration with: Philip Stamp, Nicolas laflorencie Moshe Schechter University of British.

Quantum dynamics in low dimensional systems. Anatoli Polkovnikov, Boston University AFOSR Superconductivity and Superfluidity in Finite Systems, U of Wisconsin,

Breakdown of the adiabatic approximation in low-dimensional gapless systems Anatoli Polkovnikov, Boston University Vladimir Gritsev Harvard University.

Strongly Correlated Systems of Ultracold Atoms Theory work at CUA.

From adiabatic dynamics to general questions of thermodynamics. Anatoli Polkovnikov, Boston University AFOSR R. Barankov, C. De Grandi – BU V. Gritsev.

Functional renormalization – concepts and prospects.

Functional renormalization – concepts and prospects.

Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.

Slow dynamics in gapless low-dimensional systems

Quantum dynamics in low dimensional isolated systems. Anatoli Polkovnikov, Boston University AFOSR Condensed Matter Colloquium, 04/03/2008 Roman Barankov.

Cold Atoms and Out of Equilibrium Quantum Dynamics Anatoli Polkovnikov, Boston University AFOSR Vladimir Gritsev – Harvard Ehud Altman -Weizmann Eugene.

Breakdown of the adiabatic approximation in low-dimensional gapless systems Anatoli Polkovnikov, Boston University Vladimir Gritsev Harvard University.

Quantum dynamics in low dimensional isolated systems. Anatoli Polkovnikov, Boston University AFOSR Joint Atomic Physics Colloquium, 02/27/2008 Roman Barankov.

Microscopic diagonal entropy, heat, and laws of thermodynamics Anatoli Polkovnikov, Boston University AFOSR R. Barankov, C. De Grandi – BU V. Gritsev –

Using dynamics for optical lattice simulations. Anatoli Polkovnikov, Boston University AFOSR Ehud Altman -Weizmann Eugene Demler – Harvard Vladimir Gritsev.

Functional renormalization group equation for strongly correlated fermions.

Universal adiabatic dynamics across a quantum critical point Anatoli Polkovnikov, Boston University.

Cold Atoms and Out of Equilibrium Quantum Dynamics Anatoli Polkovnikov, Boston University AFOSR Vladimir Gritsev – Harvard Ehud Altman -Weizmann Eugene.

Measuring quantum geometry From superconducting qubits to spin chains Michael Kolodrubetz, Physics Department, Boston University Theory collaborators:

U NIVERSALITY AND D YNAMIC L OCALIZATION IN K IBBLE -Z UREK Michael Kolodrubetz Boston University In collaboration with: B.K. Clark, D. Huse (Princeton)

Slow dynamics in gapless low-dimensional systems Anatoli Polkovnikov, Boston University AFOSR Vladimir Gritsev – Harvard Ehud Altman -Weizmann Eugene Demler.

Open Systems & Quantum Information Milano, 10 Marzo 2006 Measures of Entanglement at Quantum Phase Transitions M. Roncaglia G. Morandi F. Ortolani E. Ercolessi.

Chap.3 A Tour through Critical Phenomena Youjin Deng

Magnetic quantum criticality Transparencies online at Subir Sachdev.

Equilibrium dynamics of entangled states near quantum critical points Talk online at Physical Review Letters 78, 843.

Localization of phonons in chains of trapped ions Alejandro Bermúdez, Miguel Ángel Martín-Delgado and Diego Porras Department of Theoretical Physics Universidad.

Aspects of non-equilibrium dynamics in closed quantum systems K. Sengupta Indian Association for the Cultivation of Science, Kolkata Collaborators: Shreyoshi.

Presentation in course Advanced Solid State Physics By Michael Heß

Lecture 11: Ising model Outline: equilibrium theory d = 1

Integrable Models and Applications Florence, September 2003 G. Morandi F. Ortolani E. Ercolessi C. Degli Esposti Boschi F. Anfuso S. Pasini P. Pieri.

Dynamics of phase transitions in ion traps A. Retzker, A. Del Campo, M. Plenio, G. Morigi and G. De Chiara Quantum Engineering of States and Devices: Theory.

Glass Phenomenology from the connection to spin glasses: review and ideas Z.Nussinov Washington University.

Non-equilibrium critical phenomena in the chiral phase transition 1.Introduction 2.Review : Dynamic critical phenomena 3.Propagating mode in the O(N) model.

Aspects of non-equilibrium dynamics in closed quantum systems K. Sengupta Indian Association for the Cultivation of Science, Kolkata Collaborators: Diptiman.

Anatoli Polkovnikov Krishnendu Sengupta Subir Sachdev Steve Girvin Dynamics of Mott insulators in strong potential gradients Transparencies online at

Self-generated instability of a ferromagnetic quantum-critical point

Non-equilibrium dynamics of ultracold bosons K. Sengupta Indian Association for the Cultivation of Science, Kolkata Refs: Rev. Mod. Phys. 83, 863 (2011)

Order and disorder in dilute dipolar magnets

Quantum phase transition in an atomic Bose gas with Feshbach resonances M.W.J. Romans (Utrecht) R.A. Duine (Utrecht) S. Sachdev (Yale) H.T.C. Stoof (Utrecht)

Landau Theory Before we consider Landau’s expansion of the Helmholtz free Energy, F, in terms of an order parameter, let’s consider F derived from the.

Non-Fermi Liquid Behavior in Weak Itinerant Ferromagnet MnSi Nirmal Ghimire April 20, 2010 In Class Presentation Solid State Physics II Instructor: Elbio.

Quasi-1D antiferromagnets in a magnetic field a DMRG study Institute of Theoretical Physics University of Lausanne Switzerland G. Fath.

Magnetic Frustration at Triple-Axis  Magnetism, Neutron Scattering, Geometrical Frustration  ZnCr 2 O 4 : The Most Frustrated Magnet How are the fluctuating.

Entanglement generation in periodically driven integrable quantum systems K. Sengupta Theoretical Physics Department, IACS, Kolkata Collaborator: Arnab.

Quench in the Quantum Ising Model

David Pekker (U. Pitt) Gil Refael (Caltech) Vadim Oganesyan (CUNY) Ehud Altman (Weizmann) Eugene Demler (Harvard) The Hilbert-glass transition: Figuring.

MEASURING AND CHARACTERIZING THE QUANTUM METRIC TENSOR Michael Kolodrubetz, Physics Department, Boston University Equilibration and Thermalization Conference,

KITPC Max Planck Institut of Quantum Optics (Garching) Tensor networks for dynamical observables in 1D systems Mari-Carmen Bañuls.

Frustrated magnetism in 2D Collin Broholm Johns Hopkins University & NIST  Introduction Two types of antiferromagnets Experimental tools  Frustrated.

The Center for Ultracold Atoms at MIT and Harvard Strongly Correlated Many-Body Systems Theoretical work in the CUA Advisory Committee Visit, May 13-14,

Click to edit Master subtitle style 1/12/12 Non-equilibrium in cold atom systems K. Sengupta Indian Association for the Cultivation of Science, Kolkata.

Computational Physics (Lecture 10) PHY4370. Simulation Details To simulate Ising models First step is to choose a lattice. For example, we can us SC,

NTNU, April 2013 with collaborators: Salman A. Silotri (NCTU), Chung-Hou Chung (NCTU, NCTS) Sung Po Chao Helical edge states transport through a quantum.

Arnau Riera, Grup QIC, Dept. ECM, UB 16 de maig de 2009 Intoduction to topological order and topologial quantum computation.

Strong Disorder Renormalization Group

Aims of Statistical Mechanics

Coarsening dynamics Harry Cheung 2 Nov 2017.

Debasis Sadhukhan HRI, Allahabad, India

Functional Renormalization 1

Presentation transcript:

N ON - EQUILIBRIUM DYNAMIC CRITICAL SCALING OF THE QUANTUM I SING CHAIN Michael Kolodrubetz Princeton University In collaboration with: Bryan Clark, David Huse David Pekker Krishnendu Sengupta

Q UANTUM STATE OF TRANSVERSE - FIELD I SING MODEL DURING SLOW RAMP IS … Universal Non-equilibrium Experimentally viable Non-thermal Dephasing resistant

C LASSICAL P HASE T RANSITIONS “Magnetization” Landau-Ginzburg functional

C LASSICAL P HASE T RANSITIONS “Magnetization”

 Thermal fluctuations C LASSICAL P HASE T RANSITIONS

Q UANTUM P HASE T RANSITIONS One-dimensional transverse-field Ising chain

Q UANTUM P HASE T RANSITIONS One-dimensional transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)

Q UANTUM P HASE T RANSITIONS One-dimensional transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)  Quantum fluctuations

C RITICAL S CALING [Smirnov, php.math.unifi.it/users/paf/ LaPietra/files/Chelkak01.ppt]

C RITICAL S CALING [Smirnov, php.math.unifi.it/users/paf/ LaPietra/files/Chelkak01.ppt]

C RITICAL S CALING Correlation length critical exponent Dynamic critical exponent, [Smirnov, php.math.unifi.it/users/paf/ LaPietra/files/Chelkak01.ppt]

C RITICAL S CALING, Ising: Correlation length critical exponent Dynamic critical exponent

C RITICAL S CALING, Ising: Correlation length critical exponent Dynamic critical exponent Order parameter critical exponent

C RITICAL S CALING, Ising: Correlation length critical exponent Dynamic critical exponent Order parameter critical exponent

K IBBLE -Z UREK RAMPS Ramp rate

K IBBLE -Z UREK RAMPS Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS METHODIDEAWHEN IT WORKS “Old-school” Kibble-Zurek [Kibble 1976, Zurek 1985] and set the “interesting” time and length scales -Ramp to the QCP -Ramp to deep in the FM phase

K IBBLE -Z UREK RAMPS METHODIDEAWHEN IT WORKS “Old-school” Kibble-Zurek [Kibble 1976, Zurek 1985] and set the “interesting” time and length scales -Ramp to the QCP -Ramp to deep in the FM phase Kibble-Zurek scaling [Deng et. al. 2008, Erez et. al., in prep., Polkovnikov, …] Most quantities show scaling collapse when scaled by and Throughout the ramp

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate

T RANSVERSE - FIELD I SING CHAIN Sachdev: “Quantum Phase Transitions”

T RANSVERSE - FIELD I SING CHAIN Wigner fermionize Sachdev: “Quantum Phase Transitions”  phase

T RANSVERSE - FIELD I SING CHAIN Wigner fermionize Sachdev: “Quantum Phase Transitions”  phase

T RANSVERSE - FIELD I SING CHAIN Wigner fermionize Quadratic  Integrable Sachdev: “Quantum Phase Transitions”  phase

T RANSVERSE - FIELD I SING CHAIN Wigner fermionize Quadratic  Integrable Hamiltonian conserves parity for each mode k Sachdev: “Quantum Phase Transitions”  phase

T RANSVERSE - FIELD I SING CHAIN Wigner fermionize Quadratic  Integrable Hamiltonian conserves parity for each mode k Work in subspace where parity is even Sachdev: “Quantum Phase Transitions”  phase

T RANSVERSE - FIELD I SING CHAIN Wigner fermionize Quadratic  Integrable Hamiltonian conserves parity for each mode k Work in subspace where parity is even Sachdev: “Quantum Phase Transitions”  phase

T RANSVERSE - FIELD I SING CHAIN

Low energy, long wavelength theory

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate Low energy, long wavelength theory?

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate Low energy, long wavelength theory

K IBBLE -Z UREK RAMPS Adiabatic Impulse Ramp rate Low energy, long wavelength theory

K IBBLE -Z UREK SCALING LIMIT Schrödinger Equation OR Observable Fixed

K IBBLE -Z UREK SCALING LIMIT

K IBBLE -Z UREK OBSERVABLES Excess heat Spin-spin correlation function

K IBBLE -Z UREK OBSERVABLES Excess heat Spin-spin correlation function

K IBBLE -Z UREK OBSERVABLES

F INITE - SIZE SCALING

Finite size effects can be ignored

F INITE - SIZE SCALING

E QUILIBRIUM VIA DYNAMICS KZ scaling function Equilibrium scaling function If dynamic scaling functions exist, they must have the equilibrium critical exponents

F INITE - SIZE SCALING

L ANDAU -Z ENER DYNAMICS

F INITE - SIZE SCALING

L ANDAU -Z ENER DYNAMICS

A THERMAL PROPERTIES

Inverted

A THERMAL PROPERTIES Kibble-Zurek

A THERMAL PROPERTIES Kibble-Zurek Thermal

D EPHASING Protocol Ramp to create excitations Freeze the Hamiltonian Wait

D EPHASING Protocol Ramp to create excitations Freeze the Hamiltonian Wait … …

D EPHASING … … Protocol Ramp to create excitations Freeze the Hamiltonian Wait

D EPHASING … … Protocol Ramp to create excitations Freeze the Hamiltonian Wait

D EPHASING … … Protocol Ramp to create excitations Freeze the Hamiltonian Wait

D EPHASING … … Protocol Ramp to create excitations Freeze the Hamiltonian Wait

D EPHASING Dephasing in integrable model: Generalized Gibb’s ensemble (GGE) … … Protocol Ramp to create excitations Freeze the Hamiltonian Wait

D EPHASING Dephasing in integrable model: Generalized Gibb’s ensemble (GGE) … … Does dephasing occur during the Kibble- Zurek ramp?

D EPHASING Dephasing in integrable model: Generalized Gibb’s ensemble (GGE) … …

D EPHASING Dephasing in integrable model: Generalized Gibb’s ensemble (GGE) as … …

D EPHASING Dephasing in integrable model: Generalized Gibb’s ensemble (GGE) as … …

D EPHASING Cubic ramp: … …

D EPHASING Cubic ramp: as … …

D EPHASING Cubic ramp: as … …

U NIVERSALITY

Additional terms change (renormalize) the non- universal aspects of the critical point They do not change critical scaling Critical exponents Scaling functions Debated for non-integrable system dynamics

U NIVERSALITY

Paramagnet Antiferromagnet

U NIVERSALITY Paramagnet Antiferromagnet Ramp the tilt ( ) linearly in time

U NIVERSALITY

C ONCLUSIONS Solved dynamic critical scaling behavior of the TFI chain Athermal  negative correlations Phase-locked high order ramps Strong numerical evidence for universality Tilted boson model has same scaling functions Experimentally accessible Athermal features robust against open boundary conditions Open b.c. simplifies measurement Time scales already available [Simon et. al., 2007]

D EPHASING VIA QUASIPARTICLES

O PEN BOUNDARY CONDITIONS

U NIVERSALITY Remove spin ups on neighboring sites