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SciPost Physics

SciPost Physics Vol. 7 issue 1 (July 2019)

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Quantum walks on graphs of the ordered Hamming scheme and spin networks

Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet

SciPost Phys. 7, 001 (2019) · published 2 July 2019 | · pdf

It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.
Thermal counting statistics in an atomic two-mode squeezed vacuum state

Maxime Perrier, Ziyad Amodjee, Pierre Dussarrat, Alexandre Dareau, Alain Aspect, Marc Cheneau, Denis Boiron, Christoph I. Westbrook

SciPost Phys. 7, 002 (2019) · published 3 July 2019 | · pdf

We measure the population distribution in one of the atomic twin beams generated by four-wave mixing in an optical lattice. Although the produced two-mode squeezed vacuum state is pure, each individual mode is described as a statistical mixture. We confirm the prediction that the particle number follows an exponential distribution when only one spatio-temporal mode is selected. We also show that this distribution accounts well for the contrast of an atomic Hong--Ou--Mandel experiment. These experiments constitute an important validation of our twin beam source in view of a future test of a Bell inequality.
Phases of scrambling in eigenstates

Tarek Anous, Julian Sonner

SciPost Phys. 7, 003 (2019) · published 4 July 2019 | · pdf

We use the monodromy method to compute expectation values of an arbitrary number of light operators in finitely excited ("heavy") eigenstates of holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ threshold, these behave thermally up to small corrections, with an effective temperature determined by the heavy state. Below the threshold we find oscillatory and not decaying behavior. As an application of these results we compute the expectation of the out-of-time order arrangement of four light operators in a heavy eigenstate, i.e. a six-point function. Above the threshold we find maximally scrambling behavior with Lyapunov exponent $2\pi T_{\rm eff}$. Below threshold we find that the eigenstate OTOC shows persistent harmonic oscillations.
Investigating ultrafast quantum magnetism with machine learning

Giammarco Fabiani, Johan H. Mentink

SciPost Phys. 7, 004 (2019) · published 5 July 2019 | · pdf

We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a square lattice. For static properties we find close agreement with numerically exact Quantum Monte Carlo results in the thermodynamical limit. For dynamics and small systems, we find excellent agreement with exact diagonalization, while for systems up to N=256 spins close consistency with interacting spin-wave theory is obtained. In all cases the accuracy converges fast with the number of network parameters, giving access to much bigger systems than feasible before. This suggests great potential to investigate the quantum many-body dynamics of large scale spin systems relevant for the description of magnetic materials strongly out of equilibrium.
Entanglement evolution and generalised hydrodynamics: interacting integrable systems

Vincenzo Alba, Bruno Bertini, Maurizio Fagotti

SciPost Phys. 7, 005 (2019) · published 8 July 2019 | · pdf

We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.
Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice

Shenghan Jiang, Panjin Kim, Jung Hoon Han, Ying Ran

SciPost Phys. 7, 006 (2019) · published 9 July 2019 | · pdf

The properties of ground state of spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and $Z_2$ topological order leads to different types of $Z_2$ spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a $U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.
A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants

Andreas Karch, David Tong, Carl Turner

SciPost Phys. 7, 007 (2019) · published 10 July 2019 | · pdf

We describe a web of well-known dualities connecting quantum field theories in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global symmetries and includes a number of perennial favourites such as the Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac fermion, and T-duality. There are also less-loved examples, such as non-modular invariant $c=1$ CFTs that depend on a background spin structure.
Many-body localization in presence of cavity mediated long-range interactions

Piotr Sierant, Krzysztof Biedroń, Giovanna Morigi, Jakub Zakrzewski

SciPost Phys. 7, 008 (2019) · published 11 July 2019 | · pdf

We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact diagonalization and finite-size scaling. The time evolution from a random initial state exhibits features consistent with the localization picture. The dynamics can be observed with quantum gases in optical cavities, localization can be revealed through the time-dependent dynamics of the light emitted by the resonator.
QuCumber: wavefunction reconstruction with neural networks

Matthew J. S. Beach, Isaac De Vlugt, Anna Golubeva, Patrick Huembeli, Bohdan Kulchytskyy, Xiuzhe Luo, Roger G. Melko, Ejaaz Merali, Giacomo Torlai

SciPost Phys. 7, 009 (2019) · published 16 July 2019 | · pdf

As we enter a new era of quantum technology, it is increasingly important to develop methods to aid in the accurate preparation of quantum states for a variety of materials, matter, and devices. Computational techniques can be used to reconstruct a state from data, however the growing number of qubits demands ongoing algorithmic advances in order to keep pace with experiments. In this paper, we present an open-source software package called QuCumber that uses machine learning to reconstruct a quantum state consistent with a set of projective measurements. QuCumber uses a restricted Boltzmann machine to efficiently represent the quantum wavefunction for a large number of qubits. New measurements can be generated from the machine to obtain physical observables not easily accessible from the original data.
Bootstrapping MN and tetragonal CFTs in three dimensions

Andreas Stergiou

SciPost Phys. 7, 010 (2019) · published 17 July 2019 | · pdf

Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the $\varepsilon=4-d$ expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-$N$ expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the $\varepsilon$ expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the $\varepsilon$ expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups $O(2)^2\rtimes S_2$ and $O(2)^3\rtimes S_3$, a second kink is found. In the $O(2)^2\rtimes S_2$ case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO$_2$ and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the $O(2)^3\rtimes S_3$ case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.
Unimodular jordanian deformations of integrable superstrings

Stijn J. van Tongeren

SciPost Phys. 7, 011 (2019) · published 23 July 2019 | · pdf

We find new homogeneous r matrices containing supercharges, and use them to find new backgrounds of Yang-Baxter deformed superstrings. We obtain these as limits of unimodular inhomogeneous r matrices and associated deformations of AdS2 x S2 x T6 and AdS5 x S5. Our r matrices are jordanian, but also unimodular, and lead to solutions of the regular supergravity equations of motion. In general our deformations are equivalent to particular non-abelian T duality transformations. Curiously, one of our backgrounds is also equivalent to one produced by TsT transformations and an S duality transformation.
Density-operator evolution: Complete positivity and the Keldysh real-time expansion

Viktor Reimer, Maarten Rolf Wegewijs

SciPost Phys. 7, 012 (2019) · published 25 July 2019 | · pdf

We study the reduced time-evolution of open quantum systems by combining quantum-information and statistical field theory. Inspired by prior work [EPL 102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the explicit structure guaranteeing the complete positivity (CP) and trace-preservation (TP) of the real-time evolution expansion in terms of the microscopic system-environment coupling. This reveals a fundamental two-stage structure of the coupling expansion: Whereas the first stage defines the dissipative timescales of the system --before having integrated out the environment completely-- the second stage sums up elementary physical processes described by CP superoperators. This allows us to establish the nontrivial relation between the (Nakajima-Zwanzig) memory-kernel superoperator for the density operator and novel memory-kernel operators that generate the Kraus operators of an operator-sum. Importantly, this operational approach can be implemented in the existing Keldysh real-time technique and allows approximations for general time-nonlocal quantum master equations to be systematically compared and developed while keeping the CP and TP structure explicit. Our considerations build on the result that a Kraus operator for a physical measurement process on the environment can be obtained by 'cutting' a group of Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators lifted to the system plus environment which have a diagrammatic expansion in terms of time-nonlocal memory-kernel operators. These lifted Kraus operators obey coupled time-evolution equations which constitute an unraveling of the original Schr\"odinger equation for system plus environment. Whereas both equations lead to the same reduced dynamics, only the former explicitly encodes the operator-sum structure of the coupling expansion.
Out of time ordered effective dynamics of a quartic oscillator

Bidisha Chakrabarty, Soumyadeep Chaudhuri

SciPost Phys. 7, 013 (2019) · published 29 July 2019 | · pdf

We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle.
The Machine Learning landscape of top taggers

Gregor Kasieczka, Tilman Plehn, Anja Butter, Kyle Cranmer, Dipsikha Debnath, Barry M. Dillon, Malcolm Fairbairn, Darius A. Faroughy, Wojtek Fedorko, Christophe Gay, Loukas Gouskos, Jernej F. Kamenik, Patrick T. Komiske, Simon Leiss, Alison Lister, Sebastian Macaluso, Eric M. Metodiev, Liam Moore, Ben Nachman, Karl Nordström, Jannicke Pearkes, Huilin Qu, Yannik Rath, Marcel Rieger, David Shih, Jennifer M. Thompson, Sreedevi Varma

SciPost Phys. 7, 014 (2019) · published 30 July 2019 | · pdf

Based on the established task of identifying boosted, hadronically decaying top quarks, we compare a wide range of modern machine learning approaches. Unlike most established methods they rely on low-level input, for instance calorimeter output. While their network architectures are vastly different, their performance is comparatively similar. In general, we find that these new approaches are extremely powerful and great fun.