arXiv subjects

Hersh Singh

Publications and source records attributed to Hersh Singh.

22 records · Page 2Linked to original sources

arXiv2019

A qubit regularization of the $O(3)$ sigma model

We construct a qubit regularization of the $O(3)$ non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldline formulation and worm algorithms, we show that in two spatial dimensions our model has a quantum critical point where the well-known scale-invariant physics of the three-dimensional Wilson-Fisher fixed point is reproduced. In three spatial dimensions, we recover mean-field critical exponents at a similar quantum critical point. These results show that our qubit Hamiltonian is in the same universality class as the traditional classical lattice model close to the critical points. Simple modifications to our model also allow us to study the physics of traditional lattice models with $O(2)$ and $Z_2$ symmetries close to the corresponding critical points.

hep-lat↗

arXiv2018

Large-$N_c$ Relationships Among Two-Derivative Pionless Effective Field Theory Couplings

We analyze two-derivative two-nucleon interactions in a combined pionless effective field theory and large-$N_c$ expansion. At leading order in the large-$N_c$ expansion, relationships among low-energy constants emerge. We find these to be consistent with experiment. However, it is critical to correctly address the subtraction-point dependence of the low-energy constants. These results provide additional confidence that the dual-expansion procedure is useful for analyzing low-energy few-body observables.

nucl-th↗

arXiv2018

Few-body physics on a space-time lattice in the worldline approach

We formulate the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a space-time lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study non-relativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, non-relativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics

hep-lat↗

arXiv2018

Worldline approach to few-body physics on the lattice

We study the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice using the worldline formulation. By tuning the chemical potential carefully we show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector. Since fermions can be treated as hard-core bosons up to a permutation sign, we also apply this approach to non-relativistic fermions. The fermion permutation sign is treated as an observable in this approach and can be used to extract energies for each particle-number sector. Since in one dimension non-relativistic fermions can only permute due to boundary effects, unlike the auxiliary field method, in many cases our approach does not suffer from sign problems. Using our method we discover limitations of the recently proposed complex Langevin calculations in one dimension.

hep-lat↗