Phase Diagram of One-Dimensional Bosons in Disordered Potential Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman-Weizmann Yariv Kafri.

Slides:



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

Exploring Topological Phases With Quantum Walks $$ NSF, AFOSR MURI, DARPA, ARO Harvard-MIT Takuya Kitagawa, Erez Berg, Mark Rudner Eugene Demler Harvard.
Second fermionization & Diag.MC for quantum magnetism KITPC 5/12/14 AFOSR MURI Advancing Research in Basic Science and Mathematics N. Prokof’ev In collaboration.
Quantum critical states and phase transitions in the presence of non equilibrium noise Emanuele G. Dalla Torre – Weizmann Institute of Science, Israel.
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA,
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.
Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,
Subir Sachdev Science 286, 2479 (1999). Quantum phase transitions in atomic gases and condensed matter Transparencies online at
Quantum phase transitions in anisotropic dipolar magnets In collaboration with: Philip Stamp, Nicolas laflorencie Moshe Schechter University of British.
WORM ALGORITHM APPLICATIONS Nikolay Prokofiev, Umass, Amherst Boris Svistunov, Umass, Amherst Igor Tupitsyn, PITP Vladimir Kashurnikov, MEPI, Moscow Massimo.
Lattice modulation experiments with fermions in optical lattice Dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University.
Breakdown of the adiabatic approximation in low-dimensional gapless systems Anatoli Polkovnikov, Boston University Vladimir Gritsev Harvard University.
Anderson localization in BECs
ADSORPTION ISOTHERMS discontinuous jumps: layering transitions some layering transitions coexistence pressure monolayer condensation bilayer condensation.
Zero Field Superconducting Transition with Columnar Defects A. Vestergren, Mats WallinS. TeitelHans Weber KTH, StockholmUniver. RochesterLuleå Univer.
Quantum Phase Transition in Ultracold bosonic atoms Bhanu Pratap Das Indian Institute of Astrophysics Bangalore.
Quantum noise studies of ultracold atoms Eugene Demler Harvard University Funded by NSF, Harvard-MIT CUA, AFOSR, DARPA, MURI Collaborators: Ehud Altman,
Strongly Correlated Systems of Ultracold Atoms Theory work at CUA.
Interference between fluctuating condensates Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman-Weizmann Eugene Demler - Harvard Vladimir.
Fractional Quantum Hall states in optical lattices Anders Sorensen Ehud Altman Mikhail Lukin Eugene Demler Physics Department, Harvard University.
Measuring correlation functions in interacting systems of cold atoms
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov Harvard University Ehud Altman, Eugene Demler, Bertrand Halperin, Misha Lukin.
Eugene Demler Harvard University Robert Cherng, Adilet Imambekov,
Probing interacting systems of cold atoms using interference experiments Harvard-MIT CUA Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov.
Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir.
Universality in ultra-cold fermionic atom gases. with S. Diehl, H.Gies, J.Pawlowski S. Diehl, H.Gies, J.Pawlowski.
Subir Sachdev (Harvard) Philipp Werner (ETH) Matthias Troyer (ETH) Universal conductance of nanowires near the superconductor-metal quantum transition.
Non-equilibrium dynamics of cold atoms in optical lattices Vladimir Gritsev Harvard Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann.
Vortex pinning by a columnar defect in planar superconductors with point disorder Anatoli Polkovnikov Yariv Kafri, David Nelson Department of Physics,
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Takuya Kitagawa, Susanne Pielawa,
Microscopic diagonal entropy, heat, and laws of thermodynamics Anatoli Polkovnikov, Boston University AFOSR R. Barankov, C. De Grandi – BU V. Gritsev –
Quick and Dirty Introduction to Mott Insulators
Nonequilibrium dynamics of bosons in optical lattices $$ NSF, AFOSR MURI, DARPA, RFBR Harvard-MIT Eugene Demler Harvard University.
A new scenario for the metal- Mott insulator transition in 2D Why 2D is so special ? S. Sorella Coll. F. Becca, M. Capello, S. Yunoki Sherbrook 8 July.
Vladimir Gritsev Harvard Adilet Imambekov Harvard Anton Burkov Harvard Robert Cherng Harvard Anatoli Polkovnikov Harvard/Boston University Ehud Altman.
Learning about order from noise Quantum noise studies of ultracold atoms Eugene Demler Harvard University Collaborators: Takuya Kitagawa, Susanne Pielawa,
Physics of Graphene A. M. Tsvelik. Graphene – a sheet of carbon atoms The spectrum is well described by the tight- binding Hamiltonian on a hexagonal.
Probing phases and phase transitions in cold atoms using interference experiments. Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman- The.
Interference of fluctuating condensates Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir Gritsev Harvard Mikhail Lukin.
Superfluid insulator transition in a moving condensate Anatoli Polkovnikov (BU and Harvard) (Harvard) Ehud Altman, (Weizmann and Harvard) Eugene Demler,
Slow dynamics in gapless low-dimensional systems Anatoli Polkovnikov, Boston University AFOSR Vladimir Gritsev – Harvard Ehud Altman -Weizmann Eugene Demler.
Quantum simulation of low-dimensional systems using interference experiments. Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman- The Weizmann.
Dynamics of repulsively bound pairs in fermionic Hubbard model David Pekker, Harvard University Rajdeep Sensarma, Harvard University Ehud Altman, Weizmann.
Superglasses and the nature of disorder-induced SI transition
Michiel Snoek September 21, 2011 FINESS 2011 Heidelberg Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator Quenches from.
Lecture 11: Ising model Outline: equilibrium theory d = 1
F.F. Assaad. MPI-Stuttgart. Universität-Stuttgart Numerical approaches to the correlated electron problem: Quantum Monte Carlo.  The Monte.
Lecture 3. Granular superconductors and Josephson Junction arrays Plan of the Lecture 1). Superconductivity in a single grain 2) Granular superconductors:
Anatoli Polkovnikov Krishnendu Sengupta Subir Sachdev Steve Girvin Dynamics of Mott insulators in strong potential gradients Transparencies online at
Correlated States in Optical Lattices Fei Zhou (PITP,UBC) Feb. 1, 2004 At Asian Center, UBC.
Measuring correlation functions in interacting systems of cold atoms Anatoli Polkovnikov Harvard/Boston University Ehud Altman Harvard/Weizmann Vladimir.
Atoms in optical lattices and the Quantum Hall effect Anders S. Sørensen Niels Bohr Institute, Copenhagen.
Mott phases, phase transitions, and the role of zero-energy states in graphene Igor Herbut (Simon Fraser University) Collaborators: Bitan Roy (SFU) Vladimir.
Optical lattices for ultracold atomic gases Sestri Levante, 9 June 2009 Andrea Trombettoni (SISSA, Trieste)
R OLE OF D ISORDER IN S UPERCONDUCTING T RANSITION Sudhansu S. Mandal IACS, Kolkata HRI 1.
Anisotropic exactly solvable models in the cold atomic systems Jiang, Guan, Wang & Lin Junpeng Cao.
David Pekker (U. Pitt) Gil Refael (Caltech) Vadim Oganesyan (CUNY) Ehud Altman (Weizmann) Eugene Demler (Harvard) The Hilbert-glass transition: Figuring.
Hidden topological order in one-dimensional Bose Insulators Ehud Altman Department of Condensed Matter Physics The Weizmann Institute of Science With:
Probing interacting systems of cold atoms using interference experiments Vladimir Gritsev, Adilet Imambekov, Anton Burkov, Robert Cherng, Anatoli Polkovnikov,
1 Vortex configuration of bosons in an optical lattice Boulder Summer School, July, 2004 Congjun Wu Kavli Institute for Theoretical Physics, UCSB Ref:
NTNU 2011 Dimer-superfluid phase in the attractive Extended Bose-Hubbard model with three-body constraint Kwai-Kong Ng Department of Physics Tunghai University,
Spin-Orbit Coupling Effects in Bilayer and Optical Lattice Systems
ultracold atomic gases
Strong Disorder Renormalization Group
Coarsening dynamics Harry Cheung 2 Nov 2017.
Superfluid-Insulator Transition of
Ehud Altman Anatoli Polkovnikov Bertrand Halperin Mikhail Lukin
Atomic BEC in microtraps: Squeezing & visibility in interferometry
Spectroscopy of ultracold bosons by periodic lattice modulations
Presentation transcript:

Phase Diagram of One-Dimensional Bosons in Disordered Potential Anatoli Polkovnikov, Boston University Collaboration: Ehud Altman-Weizmann Yariv Kafri - Technion Gil Refael - CalTech

Dirty Bosons Bosonic atoms on disordered substrate: 4 He on Vycor Cold atoms on optical lattice Small capacitance Josephson Junction arrays Granular Superconductors

O(2) quantum rotor model Provided: In continuum systems quantum rotor model is valid after coarse-graining.

One dimension Clean limit Mapped to classical XY model in 1+1 dimensions: Superfluid Insulator K -1 y Kosterlitz-Thouless transition Universal jump in stifness:

Exponent  central contrast high Tlow T Z. Hadzibabic et. al., Observation of the BKT transition in 2D bosons, Nature (2006) Vortex proliferation Fraction of images showing at least one dislocation: 0 10% 20% 30% central contrast high T low T Jump in the correlation function exponent is related to the jump in the SF stiffness: Jump in the correlation function exponent  is related to the jump in the SF stiffness: see A.P., E. Altman, E. Demler, PNAS (2006)

No off-diagonal disorder: Real Space RG Eliminate the largest coupling: Large charging energy Large Josephson coupling E. Altman, Y. Kafri, A.P., G. Refael, PRL (2004) ( Spin chains: Dasgupta & Ma PRB 80, Fisher PRB 94, 95 ) Follow evolution of the distribution functions.

Possible phases Superfluid Clusters grow to size of chain with repeated decimation Insulator Disconnected clusters

Use parametrization Recursion relations: Assuming typical these equations are solved by simple ansatz

f 0 and g 0 obey flow equations: These equations describe Kosterlits-Thouless transition (independently confirmed by Monte-Carlo study K. G. Balabanyan, N. Prokof'ev, and B. Svistunov, PRL, 2005) Incomressible Mott Glass Superfluid f 0 ~ U Hamiltonian on the fixed line: Simple perturbative argument: weak interactions are relevant for g 0 1

Diagonal disorder is relevant!!! Transformation rule for : Next step in our approach. Consider. This is a closed subspace under the RG transformation rules. This constraint still preserves particle – hole symmetry.

New decimation rule for half-integer sites: U=  Create effective spin ½ site Other decimation rules:

Four coupled RG equations: f(  ), g , is an attractive fixed point (corresponding to relevance of diagonal disorder) N N NN = Remaining three equations are solved by an exponential ansatz Fixed points:

Number of spin ½ sites is irrelevant near the critical point! Random singlet insulator Superfluid f 0 ~ U The transition is governed by the same non-interacting critical point as in the integer case. The transition is governed by the same non-interacting critical point as in the integer case. Spin ½ sites are (dangerously) irrelevant at the critical point. Spin ½ sites are (dangerously) irrelevant at the critical point. Insulating phase is the random singlet insulator with infinite compressibility. Insulating phase is the random singlet insulator with infinite compressibility.

General story for arbitrary diagonal disorder. 1.The Sf-IN transition is governed by the non-interacting fixed point and it always belongs to KT universality class. 2.Disorder in chemical potential is dangerously irrelevant and does not affect critical properties of the transition as well as the SF phase. g0g0g0g0 f0f0f0f0

3.Insulating phase strongly depends on the type of disorder. a)Integer filling – incompressible Mott glass b)½ - integer filling – random singlet insulator with diverging compressibility c)Generic case – Bose glass with finite compressibility 4.We confirm earlier findings (Fisher et. al. 1989, Giamarchi and Schulz 1988) that there is a direct KT transition from SF to Bose glass in 1D, in particular, 5.In 1D the system restores dynamical symmetry z=1.  g 0 ~1/Log(1/J) Mottglass Boseglass Random-singletinsulator

This talk in a nutshell. Coarse-grain the system Coarse-grain the system Effective U decreases: Remaining J decrease, distribution of becomes wide Two possible scenarios: 1.U flows to zero faster than J: superfluid phase, does not matter 2.J flows to zero faster than U: insulating phase, distribution of determines the properties of the insulating phase Critical properties are the same for all possible filling factors!