Publications

Order by: publication date number of citations

• Bootstrapping traceless symmetric $O(N)$ scalars

  Marten Reehorst, Maria Refinetti, Alessandro Vichi

  SciPost Phys. 14, 068 (2023) · published 12 April 2023 | Toggle abstract · pdf

  We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indices $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case $N=4$, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model $ARP^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving $t$ and the lowest dimension scalar singlet.

  2 citations

• Coherent forward scattering as a robust probe of multifractality in critical disordered media

  Maxime Martinez, Gabriel Lemarié, Bertrand Georgeot, Christian Miniatura, Olivier Giraud

  SciPost Phys. 14, 057 (2023) · published 31 March 2023 | Toggle abstract · pdf

  We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals. We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS peak. We show that the dynamics is governed by multifractal dimensions $D_1$ and $D_2$, which suggests that CFS could be used as an experimental probe for quantum multifractality. Our predictions are universal and numerically verified in three paradigmatic models of quantum multifractality: Power-law Random Banded Matrices (PRBM), the Ruijsenaars-Schneider ensembles (RS), and the three-dimensional kicked-rotor (3DKR). In the strong multifractal regime, we show analytically that these universal predictions exactly coincide with results from standard perturbation theory applied to the PRBM and RS models.

  2 citations

• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

  Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch

  SciPost Phys. 14, 052 (2023) · published 28 March 2023 | Toggle abstract · pdf

  The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spin-spin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>-\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

  2 citations

• Variation along liquid isomorphs of the driving force for crystallization

  Ulf R. Pedersen, Karolina Adrjanowicz, Kristine Niss, Nicholas P. Bailey

  SciPost Phys. 2, 022 (2017) · published 21 June 2017 | Toggle abstract · pdf

  We investigate the variation of the driving force for crystallization of a supercooled liquid along isomorphs, curves along which structure and dynamics are invariant. The variation is weak, and can be predicted accurately for the Lennard-Jones fluid using a recently developed formalism and data at a reference temperature. More general analysis allows interpretation of experimental data for molecular liquids such as dimethyl phthalate and indomethacin, and suggests that the isomorph scaling exponent $\gamma$ in these cases is an increasing function of density, although this cannot be seen in measurements of viscosity or relaxation time.

  2 citations

• Higher-point integrands in $\mathcal{N} = 4$ super Yang-Mills theory

  Till Bargheer, Thiago Fleury, Vasco Gonçalves

  SciPost Phys. 15, 059 (2023) · published 10 August 2023 | Toggle abstract · pdf

  We compute the integrands of five-, six-, and seven-point correlation functions of twenty-prime operators with general polarizations at the two-loop order in $\mathcal{N}=4$ super Yang-Mills theory. In addition, we compute the integrand of the five-point function at three-loop order. Using the operator product expansion, we extract the two-loop four-point function of one Konishi operator and three twenty-prime operators. Two methods were used for computing the integrands. The first method is based on constructing an ansatz, and then numerically fitting for the coefficients using the twistor-space reformulation of $\mathcal{N}=4$ super Yang-Mills theory. The second method is based on the OPE decomposition. Only very few correlator integrands for more than four points were known before. Our results can be used to test conjectures, and to make progresses on the integrability-based hexagonalization approach for correlation functions.

  2 citations

• Critical properties of a comb lattice

  Natalia Chepiga, Steven R. White

  SciPost Phys. 9, 013 (2020) · published 27 July 2020 | Toggle abstract · pdf

  In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice -- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as $1/(NL)$, and not as $1/N$ or $1/L$ typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length $L$, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, $L-1$. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length $2L$.

  2 citations

• Positivity, low twist dominance and CSDR for CFTs

  Agnese Bissi, Aninda Sinha

  SciPost Phys. 14, 083 (2023) · published 25 April 2023 | Toggle abstract · pdf

  We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around $u=v=1/4$, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of $\Phi_{1,2}$ operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator ($\Delta_\sigma$) is less than $\frac{1}{2}$, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of $\Delta_\sigma$, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in $4-\epsilon$ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

  2 citations

• Entanglement Dynamics of Random GUE Hamiltonians

  Daniel Chernowitz, Vladimir Gritsev

  SciPost Phys. 10, 071 (2021) · published 19 March 2021 | Toggle abstract · pdf

  In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential $n$-point correlation functions in the gas of GUE eigenvalues.

  2 citations

• Universal suppression of superfluid weight by non-magnetic disorder in $s$-wave superconductors independent of quantum geometry and band dispersion

  Alexander Lau, Sebastiano Peotta, Dmitry I. Pikulin, Enrico Rossi, Timo Hyart

  SciPost Phys. 13, 086 (2022) · published 7 October 2022 | Toggle abstract · pdf

  Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. In particular, we consider non-magnetic disorder and $s$-wave superconductivity. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor.

  2 citations

• Massive superfluid vortices and vortex necklaces on a planar annulus

  Matteo Caldara, Andrea Richaud, Massimo Capone, Pietro Massignan

  SciPost Phys. 15, 057 (2023) · published 9 August 2023 | Toggle abstract · pdf

  We study a superfluid in a planar annulus hosting vortices with massive cores. An analytical point-vortex model shows that the massive vortices may perform radial oscillations on top of the usual uniform precession of their massless counterpart. Beyond a critical vortex mass, this oscillatory motion becomes unstable and the vortices are driven towards one of the edges. The analogy with the motion of a charged particle in a static electromagnetic field leads to the development of a plasma orbit theory that provides a description of the trajectories which remains accurate even beyond the regime of small radial oscillations. These results are confirmed by the numerical solution of coupled two-component Gross-Pitaevskii equations. The analysis is then extended to a necklace of vortices symmetrically arranged within the annulus.

  2 citations