We study the low-energy physics of the critical ( $2+1$ )-dimensional random transverse-field Ising model. The one-dimensional version of the model is a paradigmatic example of a system governed by an infinite-randomness fixed point, for which many results on the distributions of observables are known via an asymptotically exact renormalization group (RG) approach. In two dimensions, the same RG rules have been implemented numerically and demonstrate a flow to infinite randomness. However, analytical understanding of the structure of this RG has remained elusive due to the development of geometrical structure in the graph of interacting spins. To understand the character of the fixed point, we consider the RG flow acting on a joint ensemble of graphs and couplings. We propose that the RG effectively occurs in two stages: (1) randomization of the interaction graph until it belongs to a certain ensemble of random triangulations of the plane and (2) a flow of the distributions of couplings to infinite randomness while the graph ensemble remains invariant. This picture is substantiated by a numerical RG in which one obtains a steady-state graph degree distribution and subsequently infinite-randomness scaling distributions of the couplings. Both of these aspects of the RG flow can be approximately reproduced in simplified analytical models.We study the low-energy physics of the critical ($2+1$)-dimensional random transverse-field Ising model. The one-dimensional version of the model is a paradigmatic example of a system governed by an infinite-randomness fixed point, for which many results on the distributions of observables are known via an asymptotically exact renormalization group (RG) approach. In two dimensions, the same RG rules have been implemented numerically and demonstrate a flow to infinite randomness. However, analytical understanding of the structure of this RG has remained elusive due to the development of geometrical structure in the graph of interacting spins. To understand the character of the fixed point, we consider the RG flow acting on a joint ensemble of graphs and couplings. We propose that the RG effectively occurs in two stages: (1) randomization of the interaction graph until it belongs to a certain ensemble of random triangulations of the plane and (2) a flow of the distributions of couplings to infinite randomness while the graph ensemble remains invariant. This picture is substantiated by a numerical RG in which one obtains a steady-state graph degree distribution and subsequently infinite-randomness scaling distributions of the couplings. Both of these aspects of the RG flow can be approximately reproduced in simplified analytical models.

arXiv:2304.10564Physical review. B./Physical review. BAug 2, 20232 citations

Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions

Ipsita Mandal

We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields by applying a dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of U (1) and U (1) × U (1) transverse gauge couplings and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings.Our analysis allows us to treat a critical Fermi surface of a generic dimension m perturbatively in an expansion parameter = (2m)/(m + 1).One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain U (1) × U (1) theories, which was identified earlier for m = 1 at one-loop order, the third-order diagrams do.However, this fixed line feature is also obtained for m > 1, where the answer is one-loop exact due to UV/IR mixing.We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields by applying a dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of U (1) and U (1) × U (1) transverse gauge couplings and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings.Our analysis allows us to treat a critical Fermi surface of a generic dimension m perturbatively in an expansion parameter = (2m)/(m + 1).One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain U (1) × U (1) theories, which was identified earlier for m = 1 at one-loop order, the third-order diagrams do.However, this fixed line feature is also obtained for m > 1, where the answer is one-loop exact due to UV/IR mixing.

arXiv:2006.10766Physical Review ResearchNov 23, 202025 citations

The generalized point interaction in one dimension

Petr Šeba

Czechoslovak Journal of PhysicsJun 1, 1986151 citations

We study the low-energy physics of the critical (

2+1

)-dimensional random transverse-field Ising model. The one-dimensional version of the model is a paradigmatic example of a system governed by an infinite-randomness fixed point, for which many results on the distributions of observables are known via an asymptotically exact renormalization group (RG) approach. In two dimensions, the same RG rules have been implemented numerically and demonstrate a flow to infinite randomness. However, analytical understanding of the structure of this RG has remained elusive due to the development of geometrical structure in the graph of interacting spins. To understand the character of the fixed point, we consider the RG flow acting on a joint ensemble of graphs and couplings. We propose that the RG effectively occurs in two stages: (1) randomization of the interaction graph until it belongs to a certain ensemble of random triangulations of the plane and (2) a flow of the distributions of couplings to infinite randomness while the graph ensemble remains invariant. This picture is substantiated by a numerical RG in which one obtains a steady-state graph degree distribution and subsequently infinite-randomness scaling distributions of the couplings. Both of these aspects of the RG flow can be approximately reproduced in simplified analytical models.