Publications

Order by: publication date number of citations

• Scaling limit of the staggered six-vertex model with $U_q\big(\mathfrak{sl}(2)\big)$ invariant boundary conditions

  Holger Frahm, Sascha Gehrmann, Gleb Andreevich Kotousov

  SciPost Phys. 16, 149 (2024) · published 5 June 2024 | Toggle abstract · pdf

  We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An interesting feature of the lattice theory is that the spectrum of scaling dimensions contains a continuous component. By applying the ODE/IQFT correspondence and the method of the Baxter $Q$ operator the corresponding density of states is obtained. In addition, the partition function appearing in the scaling limit of the lattice model is computed, which may be of interest for the study of nonrational CFTs in the presence of boundaries. As a side result of the research, a simple formula for the matrix elements of the $Q$ operator for the general, integrable, inhomogeneous six-vertex model was discovered, that has not yet appeared in the literature. It is valid for a certain one parameter family of diagonal open boundary conditions in the sector with the $z$-projection of the total spin operator being equal to zero.

• Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model

  Veniamin A. Abalmasov

  SciPost Phys. 16, 151 (2024) · published 6 June 2024 | Toggle abstract · pdf

  Free energy as a function of polarization is calculated for the square-lattice $J_1$-$J_2$ Ising model for $J_2 < |J_1|/2$ using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at $J_2 > |J_1|/4$. These findings enrich our knowledge of the $J_1$-$J_2$ Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.

• Field theory of collinear and noncollinear magnetic order

  Oleg Tchernyshyov

  SciPost Phys. Lect. Notes 85 (2024) · published 5 September 2024 | Toggle abstract · pdf

  These lecture notes from the 2023 Summer School "Principles and applications of symmetry in magnetism" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.

• Electron addition spectral functions of low-density polaron liquids

  Alberto Nocera, Mona Berciu

  SciPost Phys. 15, 110 (2023) · published 22 September 2023 | Toggle abstract · pdf

  Spectral functions are important quantities that contain a wealth of information about the quasiparticles of a system, and that can also be measured experimentally. For systems with electron-phonon coupling, good approximations for the spectral function are available only in the Migdal limit (at Fermi energies much larger than the typical phonon frequency, $E_F\gg \Omega$, requiring a large carrier concentration $x$) and in the single polaron limit (at $x=0$). Here we show that the region with $x\ll 1$ ($E_F <\Omega$) can also be reliably investigated with the Momentum Average (MA) variational approximation, which essentially describes the formation of a polaron above an inert Fermi sea. Specifically, we show that for the one-dimensional spinless Holstein model, the MA spectral functions compare favorably with those calculated using variationally exact density matrix renormalization group simulations (DMRG) evaluated directly in frequency-space, so long as $x<0.1$ and the adiabaticity ratio $\Omega/t>0.5$. Unlike in the Migdal limit, here 'polaronic physics' emerges already at moderate couplings. The relevance of these results for a spinful low-$x$ metal is also discussed.

• Exact effective action for the O(N) vector model in the large N limit

  Han Ma, Sung-Sik Lee

  SciPost Phys. 15, 111 (2023) · published 22 September 2023 | Toggle abstract · pdf

  We present the Wilsonian effective action as a solution of the exact RG equation for the critical $O(N)$ vector model in the large $N$ limit. Below four dimensions, the exact effective action can be expressed in a closed form as a transcendental function of two leading scaling operators with infinitely many derivatives. From the exact solution that describes the RG flow from a UV theory to the fixed point theory in the IR, we obtain the mapping between UV operators and IR scaling operators. It is shown that IR scaling operators are given by sums of infinitely many UV operators with infinitely many derivatives.

• Resonating valence bonds and spinon pairing in the Dicke model

  R. Ganesh, L. Theerthagiri, G. Baskaran

  SciPost Phys. 4, 044 (2018) · published 30 June 2018 | Toggle abstract · pdf

  Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms (with states $\vert 0 \rangle$ and $\vert 1 \rangle$) coupled to a common photon mode. In the lossy cavity limit, starting with an initial state of $M$ atoms excited and $N$ atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets of the form $\frac{1}{\sqrt{2}}[\vert 0 1 \rangle - \vert 1 0 \rangle]$. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or `spinons'. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to a mixed quantum state with a fluctuating number of spinon pairs -- an inchoate superconductor. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization ($M-N$), the emission exhibits a continuous transition from a dark state to a bright state. This is reflected in the spinon pair number distribution which can be tuned from sub-poissonian to super-poissonian regimes. This opens an exciting route to simulate RVB states and superconductivity.

• (Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

  Andreas Schellenberger, Kai Phillip Schmidt

  SciPost Phys. Core 7, 038 (2024) · published 2 July 2024 | Toggle abstract · pdf

  We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst$^{++}$ [Phys. Rev. A 108, 013323 (2023)]

• Quantum oscillations in an impurity-band Anderson insulator

  Nigel R. Cooper, Jack Kelsall

  SciPost Phys. 15, 118 (2023) · published 27 September 2023 | Toggle abstract · pdf

  We show that for a system of localized electrons in an impurity band, which form an Anderson insulating state at zero temperature, there can appear quantum oscillations of the magnetization, i.e. the Anderson insulator can exhibit the de Haas-van Alphen effect. This is possible when the electronic band from which the localized states are formed has an extremum that traces out a nonzero area in reciprocal space. Our work extends existing theories for clean band insulators of this form to the situation where they host an impurity band. We show that the energies of these impurity levels oscillate with magnetic field, and compute the conditions under which these oscillations can dominate the de Haas-van Alphen effect. We discuss our results in connection with experimental measurements of quantum oscillations in Kondo insulators, and propose other experimental systems where the impurity band contribution can be dominant.

• Mesoscopic electron transport and atomic gases, a review of Frank W. J. Hekking's scientific work

  Luigi Amico, Denis M. Basko, F Sebastián Bergeret, Olivier Buisson, Hervé Courtois, Rosario Fazio, Wiebke Guichard, Anna Minguzzi, Jukka Pekola, Gerd Schön

  SciPost Phys. 5, 009 (2018) · published 27 July 2018 | Toggle abstract · pdf

  Frank W. J. Hekking performed his PhD work on "Aspects of Electron Transport in Semiconductor Nanostructures" at the TU Delft in 1992. He then worked as a postdoc at the University of Karlsruhe, the University of Minnesota, the Cavendish Laboratory at the University of Cambridge, and the Ruhr University at Bochum. In 1999 he joined the LPMMC (Laboratoire de Physique et Mod\' elisation des Milieux Condens\' es) in Grenoble and was appointed Professor at the Universit\' e Joseph Fourier and afterwards Universit\' e Grenoble Alpes. Frank Hekking was nominated as a member of the Institut Universitaire de France, for the periods 2002-2007 and 2012-2017. This review provides an overview of his scientific contributions to several fields of mesoscopic electron transport and superconductivity as well as atomic gases, and is organized along sections describing the different themes.

• Exact Mazur bounds in the pair-flip model and beyond

  Oliver Hart

  SciPost Phys. Core 7, 040 (2024) · published 4 July 2024 | Toggle abstract · pdf

  By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general $p$-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as $1/\sqrt{L}$, rather than $1/L$, as had previously been thought. This result implies that the nontrivial conserved operators implied by $p$-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.