arXiv subjects

Matheus Schossler

Publications and source records attributed to Matheus Schossler.

4 recordsLinked to original sources

arXiv2024

Infrared spectroscopy of phase transitions in the lowest Landau levels of bilayer graphene

We perform infrared magneto-spectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At $ν=4$ when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At $ν=0$ when the octet is half-filled, multiple resonances disperse non-monotonically with increasing displacement field, $D$, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted anti-ferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in $D$. When $D=0$ and $ν$ is varied, resonances at $\pmν$ show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The $ν=4$ data show good agreement with predictions from a mean-field Hartree-Fock calculation when accounting for multiple tight-binding terms in a four-band model of bilayer graphene. However even by incorporating a valley interaction anisotropy tuned to the CAFM ground state, only partial agreement is found at $ν=0$. Our results suggest additional physics is required to understand bilayer graphene at half-filling.

cond-mat.mes-hall↗

arXiv2024

Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians

The study of frustration-free Hamiltonians and their relation to finite bond-dimension matrix product states (MPS) has a long tradition. However, fractional quantum Hall (FQH) states do not quite fit into this theme since the known MPS representations of their ground states have infinite bond dimensions, which considerably obscures the relations between such MPS representations and the existence of frustration-free parent Hamiltonians. This is related to the fact that the latter necessarily are of infinite range in the orbital basis. Here, we present a theorem tailored to establishing the existence of frustration-free parent Hamiltonians in such a context. We explicitly demonstrate the utility of this theorem in the context of non-Abelian Moore-Read FQH states but argue the applicability of this theorem to transcend considerably beyond the realm of conformal-field-theory-derived MPSs or quasi-one-dimensional Hilbert spaces.

cond-mat.str-el↗

arXiv2023

From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization

We construct a recursive second-quantized formula for Moore-Read Pfaffian states. We demonstrate the utility of such second-quantized presentations by directly proving the existence of frustration-free parent Hamiltonians, without appealing to polynomial clustering properties. Furthermore, we show how this formalism is connected to the existence of a non-local order parameter for Moore-Read states and give a proof that the latter exhibit off-diagonal long-range order (ODLRO) in these quantities. We also develop a similar second-quantized presentation for the fermionic antiand PH-Pfaffian states, as well as f- and higher wave paired composite fermion states, and discuss ODLRO in most cases.

cond-mat.str-el↗

arXiv2022

Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view

We study frustration-free Hamiltonians of fractional quantum Hall (FQH) states from the point of view of the matrix product state (MPS) representation of their ground and excited states. There is a wealth of solvable models relating to FQH physics, which, however, is mostly derived and analyzed from the vantage point of first-quantized "analytic clustering properties". In contrast, one obtains long-ranged frustration-free lattice models when these Hamiltonians are studied in an orbital basis, which is the natural basis for the MPS representation of FQH states. The connection between MPS-like states and frustration-free parent Hamiltonians is the central guiding principle in the construction of solvable lattice models, but thus far, only for short-range Hamiltonians and MPSs of finite bond dimension. The situation in the FQH context is fundamentally different. Here we expose the direct link between the infinite-bond-dimension MPS structure of Laughlin-conformal field theory (CFT) states and their parent Hamiltonians. While focusing on the Laughlin state, generalizations to other CFT-MPSs will become transparent.

cond-mat.str-el↗