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SciPost Physics

SciPost Physics Vol. 9 issue 6 (December 2020)

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A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

Etienne Granet, Fabian H. L. Essler

SciPost Phys. 9, 082 (2020) · published 7 December 2020 | · pdf

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a $1/c$ expansion. The $n^{\rm th}$ term of the expansion is of order $1/c^n$ and takes into account all $\lfloor \tfrac{n}{2}\rfloor+1$ particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a ``bare" $1/c$ expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator.\\ We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order $1/c^2$. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.
Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

Philip C. Argyres, Antoine Bourget, Mario Martone

SciPost Phys. 9, 083 (2020) · published 7 December 2020 | · pdf

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an $\mathcal{N}=2$ Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic $\mathcal{N}=3$ theories.
Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures

Daniel Rohe, Carsten Honerkamp

SciPost Phys. 9, 084 (2020) · published 7 December 2020 | · pdf

We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.
Coupling quantum corrals to form artificial molecules

Saoirsé E. Freeney, Samuel T. P. Borman,Jacob W. Harteveld, Ingmar Swart

SciPost Phys. 9, 085 (2020) · published 10 December 2020 | · pdf

Quantum corrals can be considered as artificial atoms. By coupling many quantum corrals together, artificial matter can be created at will. The atomic scale precision with which the quantum corrals can be made grants the ability to tune parameters that are difficult to control in real materials, such as the symmetry of the states that couple, the on-site energy of these states, the hopping strength and the magnitude of the orbital overlap. Here, we systematically investigate the accessible parameter space for the dominant platform (CO molecules on Cu(111)) by constructing (coupled) quantum corrals of different sizes and shapes. By changing the configuration of the CO molecules that constitute the barrier between two quantum corrals, the hopping integral can be tuned between 0 and -0.3 eV for s- and p-like states, respectively. Incorporation of orbital overlap is essential to account for the experimental observations. Our results aid the design of future artificial lattices.
On scalar products in higher rank quantum separation of variables

Jean Michel Maillet, Giuliano Niccoli, Louis Vignoli

SciPost Phys. 9, 086 (2020) · published 11 December 2020 | · pdf

Using the framework of the quantum separation of variables (SoV) for higher rank quantum integrable lattice models [1], we introduce some foundations to go beyond the obtained complete transfer matrix spectrum description, and open the way to the computation of matrix elements of local operators. This first amounts to obtain simple expressions for scalar products of the so-called separate states (transfer matrix eigenstates or some simple generalization of them). In the higher rank case, left and right SoV bases are expected to be pseudo-orthogonal, that is for a given SoV co-vector, there could be more than one non-vanishing overlap with the vectors of the chosen right SoV basis. For simplicity, we describe our method to get these pseudo-orthogonality overlaps in the fundamental representations of the $\mathcal{Y}(gl_3)$ lattice model with $N$ sites, a case of rank 2. The non-zero couplings between the co-vector and vector SoV bases are exactly characterized. While the corresponding SoV-measure stays reasonably simple and of possible practical use, we address the problem of constructing left and right SoV bases which do satisfy standard orthogonality. In our approach, the SoV bases are constructed by using families of conserved charges. This gives us a large freedom in the SoV bases construction, and allows us to look for the choice of a family of conserved charges which leads to orthogonal co-vector/vector SoV bases. We first define such a choice in the case of twist matrices having simple spectrum and zero determinant. Then, we generalize the associated family of conserved charges and orthogonal SoV bases to generic simple spectrum and invertible twist matrices. Under this choice of conserved charges, and of the associated orthogonal SoV bases, the scalar products of separate states simplify considerably and take a form similar to the $\mathcal{Y}(gl_2)$ rank one case.
Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics

Shiyu Zhou, Zhi-Cheng Yang, Alioscia Hamma, Claudio Chamon

SciPost Phys. 9, 087 (2020) · published 14 December 2020 | · pdf

Clifford circuits are insufficient for universal quantum computation or creating $t$-designs with $t\ge 4$. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T $(\pi/8)$ gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.
Self-dual $S_3$-invariant quantum chains

Edward O'Brien, Paul Fendley

SciPost Phys. 9, 088 (2020) · published 16 December 2020 | · pdf

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and $S_3$, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct "Fermi velocities". The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.
Per-object systematics using deep-learned calibration

Gregor Kasieczka, Michel Luchmann, Florian Otterpohl, Tilman Plehn

SciPost Phys. 9, 089 (2020) · published 18 December 2020 | · pdf

We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets. Next, we propose a novel calibration procedure by training on labels and their error bars. Again, the network cleanly separates the different uncertainties. As a technical side effect, we show how Bayesian networks can be extended to describe non-Gaussian features.
Density scaling of generalized Lennard-Jones fluids in different dimensions

Thibaud Maimbourg, Jeppe C. Dyre, Lorenzo Costigliola

SciPost Phys. 9, 090 (2020) · published 22 December 2020 | · pdf

Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. These scaling properties do not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, the comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.
Dissipative flow equations

Lorenzo Rosso, Fernando Iemini, Marco Schirò, Leonardo Mazza

SciPost Phys. 9, 091 (2020) · published 29 December 2020 | · pdf

We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We introduce and discuss three different generators of the flow that transform a linear non-Hermitian operator into a diagonal one. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode. We then move to problems with many fermionic modes and discuss the interplay between coherent (disordered) dynamics and localized losses. Our method can also be applied to non-Hermitian Hamiltonians.
Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy

Saeed S. Jahromi, Román Orús, Didier Poilblanc, Frédéric Mila

SciPost Phys. 9, 092 (2020) · published 29 December 2020 | · pdf

We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.