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Bosonic particle-correlated states

Zhang Jiang University of New Mexico
February 06, 2014 PIRSA:14020135
Quantum Information
Introduction to Effective Field Theories - Lecture 9

Cliff Burgess McMaster University

February 07, 2014 PIRSA:14020088
13/14 PSI - Condensed Matter Review - Lecture 9

Alioscia Hamma Università degli Studi di Napoli Federico II

February 07, 2014 PIRSA:14020045
13/14 PSI - String Theory Review - Lecture 9

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 07, 2014 PIRSA:14020027
13/14 PSI - Cosmology Review - Lecture 8

Latham Boyle Perimeter Institute for Theoretical Physics

February 07, 2014 PIRSA:14020014
(0,2) correlation functions
November 23, 2004 PIRSA:04110035
Introduction to Effective Field Theories - Lecture 10

Cliff Burgess McMaster University

February 07, 2014 PIRSA:14020092
13/14 PSI - Condensed Matter Review - Lecture 10

Alioscia Hamma Università degli Studi di Napoli Federico II

February 10, 2014 PIRSA:14020046
Topological phases in graphene

Zlatko Papic University of Leeds

February 10, 2014 PIRSA:14020134
13/14 PSI - String Theory Review - Lecture 10

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 10, 2014 PIRSA:14020028
Aharonov-Bohm effect in symmetry protected states

Luiz Santos Emory University

February 10, 2014 PIRSA:14020126
13/14 PSI - Cosmology Review - Lecture 9

Latham Boyle Perimeter Institute for Theoretical Physics

February 10, 2014 PIRSA:14020017

Bosonic particle-correlated states

Zhang Jiang University of New Mexico
February 06, 2014 PIRSA:14020135
Quantum Information
Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number N. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on N or is proportional to N, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new
set of states, which constitute a natural generalization of the product-state ansatz. Our state of N=d& times;n identical particles is derived by symmetrizing the n-fold product of a d-particle quantum state. For fixed d, the parameter space of our state does not grow with N. Numerically, we show that our ansatz gives the right description for the ground state and time evolution of the two-site Bose-Hubbard model.
Introduction to Effective Field Theories - Lecture 9

Cliff Burgess McMaster University

February 07, 2014 PIRSA:14020088
13/14 PSI - Condensed Matter Review - Lecture 9

Alioscia Hamma Università degli Studi di Napoli Federico II

February 07, 2014 PIRSA:14020045
13/14 PSI - String Theory Review - Lecture 9

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 07, 2014 PIRSA:14020027
13/14 PSI - Cosmology Review - Lecture 8

Latham Boyle Perimeter Institute for Theoretical Physics

February 07, 2014 PIRSA:14020014
(0,2) correlation functions
November 23, 2004 PIRSA:04110035
Introduction to Effective Field Theories - Lecture 10

Cliff Burgess McMaster University

February 07, 2014 PIRSA:14020092
13/14 PSI - Condensed Matter Review - Lecture 10

Alioscia Hamma Università degli Studi di Napoli Federico II

February 10, 2014 PIRSA:14020046
Topological phases in graphene

Zlatko Papic University of Leeds

February 10, 2014 PIRSA:14020134

As realized for the first time in 1980s, quantum many-body systems in reduced spatial dimensions can sometimes undergo a special type of ordering which does not break any symmetry but introduces long-range entanglement and emergent excitations that have radically different properties from their original constituents. Most of our experimental knowledge of such ``topological" phases of matter comes from studies of two-dimensional electron gases in GaAs semiconductors in high magnetic fields and at low temperatures. In the first part of this talk, I will give an introduction to these systems and review some latest theoretical developments related to their entanglement properties. In the second part, I will discuss new possibilities
for experimental realizations of topological phases in bilayer graphene. I will present evidence that this material supports an ``even-denominator" fractional state, related to the Moore-Read state, whose observation has recently been reported. Finally, I will outline several proposals based on the tunability of the electron-electron interactions in bilayer graphene which might enable further experimental progress beyond GaAs.
13/14 PSI - String Theory Review - Lecture 10

Davide Gaiotto Perimeter Institute for Theoretical Physics

February 10, 2014 PIRSA:14020028
Aharonov-Bohm effect in symmetry protected states

Luiz Santos Emory University

February 10, 2014 PIRSA:14020126

Symmetry protected topological (SPT) states are generalizations of topological band insulators to interacting systems. They possess a gapped bulk spectrum together with symmetry protected edge states, with no topological order. There has been recently an intense effort to classify SPT states both in terms of group cohomology as well as from the point of view of effective field theories. An interesting related question is to understand the structute of lattice models that realize SPT physics. In this talk, I shall present a class of lattice models describing the egde of non-chiral two-dimensional bosonic SPT states protected by Z_N symmetry. A crucial aspect of the construction relies on finding the correct non-trivial Z_N symmetry realizations on the edge consistent with all the possible classes of SPT states. Then I shall discuss the Aharonov-Bohm effect on the many-body SPT state by studying this many-body effect on the aforementioned gapless edge states. The effect of a Z_N gauge flux on the egde states is formulated in terms of twisted boundary conditions of the lattice models. The low energy spectral shifts due to the gauge flux are shown to depend on each of the SPT classes in a predictable way. I shall, in the course of this talk, present numerical results of exact diagonalization of our lattice Hamiltonians that support this analysis. This work is done in collaboration with Juven Wang and
appears in arXiv:1310.8291.
13/14 PSI - Cosmology Review - Lecture 9

Latham Boyle Perimeter Institute for Theoretical Physics

February 10, 2014 PIRSA:14020017

Title	Speaker(s)	Date	Collection	Type	Info	Relevance
Bosonic particle-correlated states	Zhang Jiang	2014‑02‑06	Perimeter Institute Quantum Discussions	Scientific Series	View details	1
Introduction to Effective Field Theories - Lecture 9	Cliff Burgess	2014‑02‑07	Introduction to Effective Field Theories	Course	View details	1
13/14 PSI - Condensed Matter Review - Lecture 9	Alioscia Hamma	2014‑02‑07	13/14 PSI - Condensed Matter Review	Course	View details	1
13/14 PSI - String Theory Review - Lecture 9	Davide Gaiotto	2014‑02‑07	13/14 PSI - String Theory Review	Course	View details	1
13/14 PSI - Cosmology Review - Lecture 8	Latham Boyle	2014‑02‑07	13/14 PSI - Cosmology Review	Course	View details	1
(0,2) correlation functions		2004‑11‑23	Thematic Program on The Geometry of String Theory 2004 - 2005: Mirror Symmetry	Other	View details	1
Introduction to Effective Field Theories - Lecture 10	Cliff Burgess	2014‑02‑07	Introduction to Effective Field Theories	Course	View details	1
13/14 PSI - Condensed Matter Review - Lecture 10	Alioscia Hamma	2014‑02‑10	13/14 PSI - Condensed Matter Review	Course	View details	1
Topological phases in graphene	Zlatko Papic	2014‑02‑10	Emergence in Complex Systems	Conference	View details	1
13/14 PSI - String Theory Review - Lecture 10	Davide Gaiotto	2014‑02‑10	13/14 PSI - String Theory Review	Course	View details	1
Aharonov-Bohm effect in symmetry protected states	Luiz Santos	2014‑02‑10	Emergence in Complex Systems	Conference	View details	1
13/14 PSI - Cosmology Review - Lecture 9	Latham Boyle	2014‑02‑10	13/14 PSI - Cosmology Review	Course	View details	1

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