Publications

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• Instabilities of quantum critical metals in the limit $N_f\rightarrow0$

  Petter Säterskog

  SciPost Phys. 10, 067 (2021) · published 12 March 2021 | Toggle abstract · pdf

  We study a model in 2+1 dimensions composed of a Fermi surface of $N_f$ flavors of fermions coupled to scalar fluctuations near quantum critical points (QCPs). The $N_f\rightarrow0$ limit allows us to non-perturbatively calculate the long-range behavior of fermion correlation functions. We use this to calculate charge, spin and pair susceptibilities near different QCPs at zero and finite temperatures, with zero and finite order parameter gaps. While fluctuations smear out the fermionic quasiparticles, we find QCPs where the overall effect of fluctuations leads to enhanced pairing. We also find QCPs where the fluctuations induce spin and charge density wave instabilities for a finite interval of order parameter fluctuation gaps at $T=0$. We restore a subset of the diagrams suppressed in the $N_f\rightarrow0$ limit, all diagrams with internal fermion loops with at most 2 vertices, and find that this does not change the long-range behavior of correlators except right at the QCPs.

  1 citation

• Weak topological insulating phases of hard-core-bosons on the honeycomb lattice

  Amrita Ghosh, Eytan Grosfeld

  SciPost Phys. 10, 059 (2021) · published 9 March 2021 | Toggle abstract · pdf

  We study the phases of hard-core-bosons on a two-dimensional periodic honeycomb lattice in the presence of an on-site potential with alternating sign along the different y-layers of the lattice. Using quantum Monte Carlo simulations supported by analytical calculations, we identify a weak topological insulator, characterized by a zero Chern number but non-zero Berry phase, which is manifested at either density 1/4 or 3/4, as determined by the potential pattern. Additionally, a charge-density-wave insulator is observed at 1/2-filling, whereas the phase diagram at intermediate densities is occupied by a superfluid phase. The weak topological insulator is further shown to be robust against any amount of nearest-neighbor repulsion, as well as weak next-nearest-neighbor repulsion. The experimental realization of our model is feasible in an optical lattice setup.

  3 citations

• Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

  Thomas Köhler, Jan Stolpp, Sebastian Paeckel

  SciPost Phys. 10, 058 (2021) · published 9 March 2021 | Toggle abstract · pdf

  Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix\hyp product\hyp state representation and the single\hyp site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to $L=501$ while accounting for $N_{\rm ph}=63$ phonons per site with high precision in the CDW phase.

  18 citations

• Spin-polarized two-dimensional electron/hole gases on LiCoO$_2$ layers.

  Santosh Kumar Radha, Walter R. L. Lambrecht

  SciPost Phys. 10, 057 (2021) · published 8 March 2021 | Toggle abstract · pdf

  First-principles calculations show the formation of a 2D spin polarized electron (hole) gas on the Li (CoO$_2$) terminated surfaces of finite slabs down to a monolayer, in remarkable contrast with the bulk band structure, which is stabilized by Li donating its electron to the CoO$_2$ layer forming a Co-$d-t_{2g}^6$ insulator. By mapping the first-principles computational results to a minimal tight-binding models corresponding to a non-chiral 3D generalization of the quadripartite Su-Schrieffer-Heeger (SSH4) model and symmetry analysis, we show that these surface states have topological origin.

  3 citations

• Entanglement gap, corners, and symmetry breaking

  Vincenzo Alba

  SciPost Phys. 10, 056 (2021) · published 8 March 2021 | Toggle abstract · pdf

  We investigate the finite-size scaling of the lowest entanglement gap $\delta\xi$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $\delta\xi=\Omega/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $\delta\xi=\pi^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $\Omega$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $\Omega$, at least for the case of a square corner.

  5 citations

• Finite-size corrections in critical symmetry-resolved entanglement

  Benoit Estienne, Yacine Ikhlef, Alexi Morin-Duchesne

  SciPost Phys. 10, 054 (2021) · published 4 March 2021 | Toggle abstract · pdf

  In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

  45 citations

• Floquet conformal field theories with generally deformed Hamiltonians

  Ruihua Fan, Yingfei Gu, Ashvin Vishwanath, Xueda Wen

  SciPost Phys. 10, 049 (2021) · published 25 February 2021 | Toggle abstract · pdf

  In this work, we study non-equilibrium dynamics in Floquet conformal field theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the energy-momentum density spatially modulated by an arbitrary smooth function. This generalizes earlier work which was restricted to the sine-square deformed type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra. Here we show remarkably that the problem remains soluble in this generalized case which involves the full Virasoro algebra, based on a geometrical approach. It is found that the phase diagram is determined by the stroboscopic trajectories of operator evolution. The presence/absence of spatial fixed points in the operator evolution indicates that the driven CFT is in a heating/non-heating phase, in which the entanglement entropy grows/oscillates in time. Additionally, the heating regime is further subdivided into a multitude of phases, with different entanglement patterns and spatial distribution of energy-momentum density, which are characterized by the number of spatial fixed points. Phase transitions between these different heating phases can be achieved simply by changing the duration of application of the driving Hamiltonian. We demonstrate the general features with concrete CFT examples and compare the results to lattice calculations and find remarkable agreement.

  16 citations

• A beginner's guide to non-abelian iPEPS for correlated fermions

  Benedikt Bruognolo, Jheng-Wei Li, Jan von Delft, Andreas Weichselbaum

  SciPost Phys. Lect. Notes 25 (2021) · published 25 February 2021 | Toggle abstract · pdf

  Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension $D=24$ on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with $2$ bands of spinful fermions of $\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$ symmetry, the other with $3$ flavors of spinless fermions of $\mathrm{SU}(3)_\mathrm{flavor}$ symmetry.

  9 citations

• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

  Dainius Kilda, Alberto Biella, Marco Schirò, Rosario Fazio, Jonathan Keeling

  SciPost Phys. Core 4, 005 (2021) · published 24 February 2021 | Toggle abstract · pdf

  We present calculations of the time-evolution of the driven-dissipative XYZ model using the infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. We explore the conditions under which this approach reaches a steady state. In particular, we study the conditions where apparently converged calculations may become unstable with increasing bond dimension of the tensor-network ansatz. We discuss how more reliable results could be obtained.

  11 citations

• Non-unitary dynamics of Sachdev-Ye-Kitaev chain

  Chunxiao Liu, Pengfei Zhang, Xiao Chen

  SciPost Phys. 10, 048 (2021) · published 23 February 2021 | Toggle abstract · pdf

  We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large $N$ limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

  30 citations