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SciPost Physics

SciPost Physics Vol. 8 issue 3 (March 2020)

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Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

Hendrik Hobrecht, Alfred Hucht

SciPost Phys. 8, 032 (2020) · published 2 March 2020 | · pdf

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.
Algebraic structure of classical integrability for complex sine-Gordon

Jean Avan, Luc Frappat, Eric Ragoucy

SciPost Phys. 8, 033 (2020) · published 2 March 2020 | · pdf

The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.
Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz

György Z. Fehér, Balázs Pozsgay

SciPost Phys. 8, 034 (2020) · published 3 March 2020 | · pdf

The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable lattice models solvable by the nested Bethe Ansatz, with group symmetry $SU(N)$, $N\ge 3$. In these models the Bethe Ansatz involves various types of Bethe rapidities corresponding to the "nesting" procedure, describing the internal degrees of freedom for the excitations. We show that a complete set of charges for the GGE can be obtained from the known fusion hierarchy of transfer matrices. The resulting charges are quasi-local in a certain regime in rapidity space, and they completely fix the rapidity distributions of each string type from each nesting level.
Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line

Alexandre Krajenbrink, Pierre Le Doussal

SciPost Phys. 8, 035 (2020) · published 4 March 2020 | · pdf

We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at $x=0$ either repulsive $A>0$, or attractive $A<0$. We provide an exact solution, using replica Bethe ansatz methods, to two problems which were recently proved to be equivalent [Parekh, arXiv:1901.09449]: the droplet initial condition for arbitrary $A \geqslant -1/2$, and the Brownian initial condition with a drift for $A=+\infty$ (infinite hard wall). We study the height at $x=0$ and obtain (i) at all time the Laplace transform of the distribution of its exponential (ii) at infinite time, its exact probability distribution function (PDF). These are expressed in two equivalent forms, either as a Fredholm Pfaffian with a matrix valued kernel, or as a Fredholm determinant with a scalar kernel. For droplet initial conditions and $A> - \frac{1}{2}$ the large time PDF is the GSE Tracy-Widom distribution. For $A= \frac{1}{2}$, the critical point at which the DP binds to the wall, we obtain the GOE Tracy-Widom distribution. In the critical region, $A+\frac{1}{2} = \epsilon t^{-1/3} \to 0$ with fixed $\epsilon = \mathcal{O}(1)$, we obtain a transition kernel continuously depending on $\epsilon$. Our work extends the results obtained previously for $A=+\infty$, $A=0$ and $A=- \frac{1}{2}$.
Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

Oleksandr Gamayun, Oleg Lychkovskiy, Jean-Sébastien Caux

SciPost Phys. 8, 036 (2020) · published 5 March 2020 | · pdf

We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.
Front dynamics in the XY chain after local excitations

Viktor Eisler, Florian Maislinger

SciPost Phys. 8, 037 (2020) · published 6 March 2020 | · pdf

We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.
Number-resolved imaging of $^{88}$Sr atoms in a long working distance optical tweezer

Niamh Christina Jackson, Ryan Keith Hanley, Matthew Hill, Frédéric Leroux, Charles S. Adams, Matthew Philip Austin Jones

SciPost Phys. 8, 038 (2020) · published 10 March 2020 | · pdf

We demonstrate number-resolved detection of individual strontium atoms in a long working distance low numerical aperture (NA = 0.26) tweezer. Using a camera based on single-photon counting technology, we determine the presence of an atom in the tweezer with a fidelity of 0.989(6) (and loss of 0.13(5)) within a 200 $\mu$s imaging time. Adding continuous narrow-line Sisyphus cooling yields similar fidelity, at the expense of much longer imaging times (30 ms). Under these conditions we determine whether the tweezer contains zero, one or two atoms, with a fidelity $>$0.8 in all cases with the high readout speed of the camera enabling real-time monitoring of the number of trapped atoms. Lastly we show that the fidelity can be further improved by using a pulsed cooling/imaging scheme that reduces the effect of camera dark noise.
Decaying quantum turbulence in a two-dimensional Bose-Einstein condensate at finite temperature

Andrew J. Groszek, Matthew J. Davis, Tapio P. Simula

SciPost Phys. 8, 039 (2020) · published 12 March 2020 | · pdf

We numerically model decaying quantum turbulence in two-dimensional disk-shaped Bose-Einstein condensates, and investigate the effects of finite temperature on the turbulent dynamics. We prepare initial states with a range of condensate temperatures, and imprint equal numbers of vortices and antivortices at randomly chosen positions throughout the fluid. The initial states are then subjected to unitary time-evolution within the c-field methodology. For the lowest condensate temperatures, the results of the zero temperature Gross-Pitaevskii theory are reproduced, whereby vortex evaporative heating leads to the formation of Onsager vortex clusters characterised by a negative absolute vortex temperature. At higher condensate temperatures the dissipative effects due to vortex-phonon interactions tend to drive the vortex gas towards positive vortex temperatures dominated by the presence of vortex dipoles. We associate these two behaviours with the system evolving toward an anomalous non-thermal fixed point, or a Gaussian thermal fixed point, respectively.
Quantum coherence from commensurate driving with laser pulses and decay

Goetz S. Uhrig

SciPost Phys. 8, 040 (2020) · published 12 March 2020 | · pdf

Non-equilibrium physics is a particularly fascinating field of current research. Generically, driven systems are gradually heated up so that quantum effects die out. In contrast, we show that a driven central spin model including controlled dissipation in a highly excited state allows us to distill quantum coherent states, indicated by a substantial reduction of entropy. The model is experimentally accessible in quantum dots or molecules with unpaired electrons. The potential of preparing and manipulating coherent states by designed driving potentials is pointed out.
Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

Frederik S. Møller, Jörg Schmiedmayer

SciPost Phys. 8, 041 (2020) · published 13 March 2020 | · pdf

We present an open-source Matlab framework, titled iFluid, for simulating the dynamics of integrable models using the theory of generalized hydrodynamics (GHD). The framework provides an intuitive interface, enabling users to define and solve problems in a few lines of code. Moreover, iFluid can be extended to encompass any integrable model, and the algorithms for solving the GHD equations can be fully customized. We demonstrate how to use iFluid by solving the dynamics of three distinct systems: (i) The quantum Newton's cradle of the Lieb-Liniger model, (ii) a gradual field release in the XXZ-chain, and (iii) a partitioning protocol in the relativistic sinh-Gordon model.
Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

Xhek Turkeshi, Marcello Dalmonte

SciPost Phys. 8, 042 (2020) · published 16 March 2020 | · pdf

Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental simulation of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave-functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement content. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories - as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.
Multi-scale mining of kinematic distributions with wavelets

Ben G. Lillard, Tilman Plehn, Alexis Romero, Tim M. P. Tait

SciPost Phys. 8, 043 (2020) · published 17 March 2020 | · pdf

Typical LHC analyses search for local features in kinematic distributions. Assumptions about anomalous patterns limit them to a relatively narrow subset of possible signals. Wavelets extract information from an entire distribution and decompose it at all scales, simultaneously searching for features over a wide range of scales. We propose a systematic wavelet analysis and show how bumps, bump-dip combinations, and oscillatory patterns are extracted. Our kinematic wavelet analysis kit KWAK provides a publicly available framework to analyze and visualize general distributions.
Yang-Baxter integrable Lindblad equations

Aleksandra A. Ziolkowska, Fabian H.L. Essler

SciPost Phys. 8, 044 (2020) · published 19 March 2020 | · pdf

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.
Entanglement spreading and quasiparticle picture beyond the pair structure

Alvise Bastianello, Mario Collura

SciPost Phys. 8, 045 (2020) · published 20 March 2020 | · pdf

The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations' pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work, we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Renyi entropies. Our results are in perfect agreement with iTEBD numerical simulations.
Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

Sara Murciano, Giuseppe Di Giulio, Pasquale Calabrese

SciPost Phys. 8, 046 (2020) · published 26 March 2020 | · pdf

We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.
Superfluids as higher-form anomalies

Luca V. Delacrétaz, Diego M. Hofman, Grégoire Mathys

SciPost Phys. 8, 047 (2020) · published 26 March 2020 | · pdf

We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid — its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higher-form symmetries and their anomalies instead of how the symmetries are realized. This treatment is more general and, in particular, includes the case of BKT transitions. As an application of this formalism we construct the hydrodynamic theories of conventional (0-form) and 1-form superfluids.
Locally quasi-stationary states in noninteracting spin chains

Maurizio Fagotti

SciPost Phys. 8, 048 (2020) · published 27 March 2020 | · pdf

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").