Publications

Order by: publication date number of citations

• Extreme boundary conditions and random tilings

  Jean-Marie Stéphan

  SciPost Phys. Lect. Notes 26 (2021) · published 12 March 2021 | Toggle abstract · pdf

  Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as illustrated by the famous 'arctic circle theorem' for dimer coverings in two dimensions. In these notes, I discuss such examples in the context of critical phenomena, and their relation to 1+1d quantum particle models. All those turn out to share a common feature: they are inhomogeneous, in the sense that local densities now depend on position in the bulk. I explain how such problems may be understood using variational (or hydrodynamic) arguments, how to treat long range correlations, and how non trivial edge behavior can occur. While all this is done on the example of the dimer model, the results presented here have much greater generality. In that sense the dimer model serves as an opportunity to discuss broader methods and results. [These notes require only a basic knowledge of statistical mechanics.]

  12 citations

• Conformal partial waves in momentum space

  Marc Gillioz

  SciPost Phys. 10, 081 (2021) · published 13 April 2021 | Toggle abstract · pdf

  The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension $d \geq 3$ (including non-integer $d$). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in $d = 4$ dimensions.

  12 citations

• A microscopic realization of dS$_3$

  Scott Collier, Lorenz Eberhardt, Beatrix Mühlmann

  SciPost Phys. 18, 131 (2025) · published 17 April 2025 | Toggle abstract · pdf

  We propose a precise duality between pure de Sitter quantum gravity in $2+1$ dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlators of massive particles in the universe specified by this wavefunction. Integrating these correlators over the metric at future infinity yields gauge-invariant observables, which are identified with the string amplitudes of the complex Liouville string [S. Collier et al., arXiv: 2409.17246]. This establishes a direct connection between integrated cosmological correlators and the resolvents of the matrix integral dual to the complex Liouville string, thereby demonstrating one aspect of the dS$_3$/matrix integral duality. The second aspect concerns the cosmological horizon of the dS static patch and the Gibbons-Hawking entropy it is conjectured to encode. We show that this entropy can be reproduced exactly by counting the entries of the matrix.

  12 citations

• Emergent orbital magnetization in Kitaev quantum magnets

  Saikat Banerjee, Shi-Zeng Lin

  SciPost Phys. 14, 127 (2023) · published 24 May 2023 | Toggle abstract · pdf

  Unambiguous identification of the Kitaev quantum spin liquid (QSL) in materials remains a huge challenge despite many encouraging signs from various measurements. To facilitate the experimental detection of the Kiteav QSL, here we propose to use remnant charge response in Mott insulators hosting QSL to identify the key signatures of QSL. We predict an emergent orbital magnetization in a Kitaev system in an external magnetic field. The direction of the orbital magnetization can be flipped by rotating the external magnetic field in the honeycomb plane. The orbital magnetization is demonstrated explicitly through a detailed microscopic analysis of the multiorbital Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture. We first derive the localized electrical loop current operator in terms of the spin degrees of freedom. Thereafter, utilizing the Majorana representation, we estimate the loop currents in the ground state of the chiral Kitaev QSL state, and obtain the consequent current textures, which are responsible for the emergent orbital magnetization. Finally, we discuss the possible experimental techniques to visualize the orbital magnetization which can be considered as the signatures of the underlying excitations.

  12 citations

• Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

  Izaak Neri, Matteo Polettini

  SciPost Phys. 14, 131 (2023) · published 25 May 2023 | Toggle abstract · pdf

  The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

  12 citations

• The antiferromagnetic $S=1/2$ Heisenberg model on the C$_{60}$ fullerene geometry

  Roman Rausch, Cassian Plorin, Matthias Peschke

  SciPost Phys. 10, 087 (2021) · published 23 April 2021 | Toggle abstract · pdf

  We solve the quantum-mechanical antiferromagnetic Heisenberg model with spins positioned on vertices of the truncated icosahedron using the density-matrix renormalization group (DMRG). This describes magnetic properties of the undoped C$_{60}$ fullerene at half filling in the limit of strong on-site interaction $U$. We calculate the ground state and correlation functions for all possible distances, the lowest singlet and triplet excited states, as well as thermodynamic properties, namely the specific heat and spin susceptibility. We find that unlike smaller C$_{20}$ or C$_{32}$ that are solvable by exact diagonalization, the lowest excited state is a triplet rather than a singlet, indicating a reduced frustration due to the presence of many hexagon faces and the separation of the pentagonal faces, similar to what is found for the truncated tetrahedron. This implies that frustration may be tuneable within the fullerenes by changing their size. The spin-spin correlations are much stronger along the hexagon bonds and exponentially decrease with distance, so that the molecule is large enough not to be correlated across its whole extent. The specific heat shows a high-temperature peak and a low-temperature shoulder reminiscent of the kagomé lattice, while the spin susceptibility shows a single broad peak and is very close to the one of C$_{20}$.

  12 citations

• Relating non-Hermitian and Hermitian quantum systems at criticality

  Chang-Tse Hsieh, Po-Yao Chang

  SciPost Phys. Core 6, 062 (2023) · published 12 September 2023 | Toggle abstract · pdf

  We demonstrate three types of transformations that establish connections between Hermitian and non-Hermitian quantum systems at criticality, which can be described by conformal field theories (CFTs). For the transformation preserving both the energy and the entanglement spectra, the corresponding central charges obtained from the logarithmic scaling of the entanglement entropy are identical for both Hermitian and non-Hermitian systems. The second transformation, while preserving the energy spectrum, does not perserve the entanglement spectrum. This leads to different entanglement entropy scalings and results in different central charges for the two types of systems. We demonstrate this transformation using the dilation method applied to the free fermion case. Through this method, we show that a non-Hermitian system with central charge $c = -4$ can be mapped to a Hermitian system with central charge $c = 2$. Lastly, we investigate the Galois conjugation in the Fibonacci model with the parameter $\phi \to - 1/\phi$, in which the transformation does not preserve both energy and entanglement spectra. We demonstrate the Fibonacci model and its Galois conjugation relate the tricritical Ising model/3-state Potts model and the Lee-Yang model with negative central charges from the scaling property of the entanglement entropy.

  12 citations

• "Spectrally gapped" random walks on networks: a Mean First Passage Time formula

  Silvia Bartolucci, Fabio Caccioli, Francesco Caravelli, Pierpaolo Vivo

  SciPost Phys. 11, 088 (2021) · published 4 November 2021 | Toggle abstract · pdf

  We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices $H=\langle H\rangle +\delta H$, with $\langle H\rangle$ rank-$1$ and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement.

  12 citations

• Coexistence of coarsening and mean field relaxation in the long-range Ising chain

  Federico Corberi, Alessandro Iannone, Manoj Kumar, Eugenio Lippiello, Paolo Politi

  SciPost Phys. 10, 109 (2021) · published 18 May 2021 | Toggle abstract · pdf

  We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance $r$ decaying as $r^{-\alpha}$. For $\alpha =0$, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with $\alpha >1$ there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. $0<\alpha <1$, we show that the system shows both features, with probability $P_\alpha (N)$ of having the latter one, with the different limiting behaviours $\lim _{N\to \infty}P_\alpha (N)=0$ (at fixed $\alpha<1$) and $\lim _{\alpha \to 1}P_\alpha (N)=1$ (at fixed finite $N$). {\color{red}We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time $\tau _\alpha (N)\sim N^\alpha$.

  12 citations

• Symmetries and anomalies of Kitaev spin-S models: Identifying symmetry-enforced exotic quantum matter

  Ruizhi Liu, Ho Tat Lam, Han Ma, Liujun Zou

  SciPost Phys. 16, 100 (2024) · published 9 April 2024 | Toggle abstract · pdf

  We analyze the internal symmetries and their anomalies in the Kitaev spin-$S$ models. Importantly, these models have a lattice version of a $\mathbb{Z}_2$ 1-form symmetry, denoted by $\mathbb{Z}_2^{[1]}$. There is also an ordinary 0-form $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T$ symmetry, where $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}$ are $\pi$ spin rotations around two orthogonal axes, and $\mathbb{Z}_2^T$ is the time reversal symmetry. The anomalies associated with the full $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T×\mathbb{Z}_2^{[1]}$ symmetry are classified by $\mathbb{Z}_2^{17}$. We find that for $S∈\mathbb{Z}$ the model is anomaly-free, while for $S∈\mathbb{Z}+\frac{1}{2}$ there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these symmetries and anomalies apply to not only the Kitaev spin-$S$ models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, generically these consequences still apply even if the perturbations break the 1-form symmetry. A notable consequence is that there should generically be a deconfined fermionic excitation carrying no fractional quantum number under the $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T$ symmetry if $S∈\mathbb{Z}+\frac{1}{2}$, which implies symmetry-enforced exotic quantum matter. We also discuss the consequences for $S∈\mathbb{Z}$.

  12 citations