# Quantum Dynamics of Low-Dimensional Systems Workshop

In memoriam

"You should strive to solve the most challenging problem and get a result which is most valuable from the intellectual
point of view. You cannot try to publish every paper in the best possible journal. There is simply too little time."

Dates: September 21st and 22nd, 2013

Location: 17 Oxford Street, Jefferson Lab room 250, Cambridge, MA 02138 (map)

Information/Scheduling: Jennifer Bastin

### Tentative schedule

 Saturday 21 September 2013 9:20–9:30am Workshop Opening 9:30–10:15 Eugene Demler 10:15–11:00 Aditya Shashi 11:00–11:45 J.S. Caux 11:45–1:00pm Lunch 1:00–1:45  Bertrand Halperin 1:45–2:30  Anatoli Polkovnikov 2:30–3:15  Subir Sachdev 3:15–4:00  Refreshments 4:00–4:45 Alexey Tsvelik 4:45–5:30 Jun Kono 5:30–6:00 Onlasyn Imambekov Sunday 22 September 2013 9:00–9:45am Karyn Le Hur 9:45–10:30 Mohammad Hafezi 10:30–11:30  Refreshments/Discussion 11:30–12:15pm Joerg Schmiedmeyer 12:15–1:00  Matteo Rizzi 1:00–2:00 Lunch 2:00–2:45 Lev Ioffe 2:45–3:30 Alexey Gorshkov 3:30–4:15 Refreshments 4:15–5:00 Ryan Barnett 5:00–5:45 Leonid Glazman

### Participants (with titles & abstracts as provided):

Lev Ioffe (Rutgers)
Title:
Josephson ladders implementing quantum critical one-dimensional model and their applications.

Abstract: I present the novel type of Josephson ladders that can be mapped onto the quantum one dimensional models with tunable criticality and their applications for the implementation of a tunable superinductor, the element that is characterized by a purely inductive response and impedance much larger than quantum (6.5 kOm). In particular I will show the ladders that allow an experimental realization of the one dimensional φ4 theory with the mass that changes sign with magnetic field. Close to the critical point the low energy excitations in this theory can be described by Ising model in transverse field. The solution of this model shows that these excitations are Majorana fermions. I will show the spectroscopy data that display the spectral lines that are due to these fermionic excitations. I also show that slight variation of the ladder design allows one to implement other Hamiltonians that can be mapped to different quantum critical models. The applications of these ladders range from the current standard to the studies of the non-equilibrium properties of almost integrable quantum problems.

Jun Kono (Rice)
Title: Superfluorescence from a Quantum-Degenerate Two-Dimensional Electron-Hole Gas

Matteo Rizzi (Mainz)
Title:
Robustness of quantum memories based on Majorana zero modes

Abstract: We analyze the rate at which quantum information encoded in zero-energy Majorana modes is lost in the presence of perturbations. We find that under certain conditions it can survive for times that scale exponentially with the size of the chain, for both quenching and time-dependent dephasing perturbations, even when the latter have spectral components above the system's energy gap. The origin of the robust storage, namely the fact that a sudden quench aects in the same way both parity sectors of the original spectrum, is discussed, together with the memory performance at finite temperatures and in the presence of particle exchange with a bath.

Alexei Tsvelik (Brookhaven)
Title:
A tractable model of bad metals

Abstract: We discuss the model Kondo type Hamiltonian representing an analytically tractable version of the model used by Yin {\it et.al.}, Phys. Rev. B{\bf 86}, 2399 (2012) to explain a non-Fermi liquid behavior of iron chalcogenides and ruthenates in the intermediate energy region. It is suggested that the complete screening of the local degrees of freedom proceeds in two stages described by two characteristic temperatures $T_K^{orb} >> \epsilon^*$. The first energy scale marks a screening of the orbital degrees of freedom and the second one marks a crossover to the regime with coherent propagation of quasiparticles. Our calculations show that the latter regime is not a Landau Fermi liquid since the imaginary part of the electron self energy $\Im m\Sigma(\omega) \sim \omega^{b}, ~~ 1< b <2$.

Karyn Le Hur (Paris)
Title:
Dissipative and Non-Equilibrium Spin-Boson Systems

Abstract: In this Talk, we focus on Entanglement and Dynamical properties of Spin-Boson Systems consisting of Spins coupled to Bosonic Environments.  The case of a boson bath with Ohmic dissipation will be thoroughly addressed with applications in Cold Atoms and Photon Systems for example. This case is particularly interesting since it reveals a quantum phase transition, non-trivial features in the spin dynamics and connections with other models such as the Kondo model and the Ising model with long-range forces. Entanglement properties of the system can be exactly evaluated using the Bethe Ansatz approach. Concerning driven Spin-Boson systems, we apply the non-perturbative stochastic scheme discussed in the paper, P. P. Orth, A. Imambekov and K. Le Hur, Phys. Rev. B 87, 014305 (2013) and address a few applications.

Title:
Interaction quench in the 1D Bose gas

Abstract: We obtain results on interaction quenches in a non-quadratic continuum system, the 1D Bose gas described by the integrable Lieb-Liniger model, and we show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble. I will briefly describe how we take into account the conserve charges associated with the integrability of the model to formulate the Generalized Gibbs Ensemble which correctly predicts the asymptotic steady state.

Anatoli Polkovnikov
Title: Classifying and measuring geometry of quantum phases

Abstract: Using transverse field Ising model as a primary example I will show that its phase diagram can be characterized using Riemannian geometry based on the Fubini-Study metric. I will show there are robust geometric invariants based on the integrated Gauss curvature, which are protected against small perturbations. I will show that one can classify critical points and special singular symmetry directions  based on the independent of parametrization Gauss curvature. I will identify three generic types of singularities: removable, conical and curvature. At the end I will discuss how the metric tensor can be measured as a standard dynamical response and as a leading non-adiabatic response in energy.

Joerg Schmiedmayer (Vienna Center for Quantum Science and Technology (VCQ), Atominstitut, TU-Wien)

Title: How does an isolated 1d quantum system relax?

Abstract: One of the biggest challenges in probing non-equilibrium dynamics of many-body quantum systems is that there is no general approach to characterize the resulting quantum states. Interference experiments give access to the phase of the order parameter. The full distribution functions of the interference amplitude [1,2], and the full phase correlation functions allows us to study the relaxation dynamics in one-dimensional quantum systems. Starting form a coherently split 1d quantum gas, the initial coherence slowly dies.  Due to the approximate conserved quantities in our nearly integrable system,  this relaxation leads to a pre-thermalized state [3], which is characterized by thermal like distribution functions but exhibits an effective temperature much lower than the kinetic temperature of the initial system.  A detailed study of the correlation functions reveals that these thermal-like properties emerge locally in their final form and propagate through the system in a light-cone-like evolution [4].

[1] A. Polkovnikov, et al. PNAS 103, 6125 (2006); V. Gritsev, et al., Nature Phys. 2, 705 (2006);
[2] S. Hofferberth et al. Nature Physics 4, 489 (2008);
[4] M. Gring et al., Science 337, 1318 (2012); D. Adu Smith et al. NJP 15, 075011 (2013).
[5] T. Langen et al. Nature Physics DOI: 10.1038/nphys2739 (2013)  arXiv:1305.3708.

Onlasyn Imambekov & Aigerim Kabdiyeva (Almaty)

Leonid Glazman (Yale)

Alexey Gorshkov (NIST)

Title: Propagation of information in systems with long-range interactions

Misha Lukin (Harvard)

Subir Sachdev (Harvard)

Title: Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors

Abstract: The hole-doped cuprate high temperature superconductors enter the pseudogap regime as their superconducting critical temperature, T_c, falls with decreasing hole density. Experiments have probed this regime for over two decades, but we argue that decisive new information has emerged from recent X-ray scattering experiments. The experiments observe incommensurate charge density wave fluctuations whose strength rises gradually over a wide temperature above T_c, but then decreases as the temperature is lowered below T_c. We propose a theory in which the superconducting and charge-density wave orders exhibit angular fluctuations in a 6-dimensional space. The theory provides a natural quantitative fit to the X-ray data, and is consistent with other observed characteristics of the pseudogap.