Some group theoretical aspects of the interacting boson-fermion model

The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place three-particles, two identical and one impurity, in an axial symmetric harmonic trap and solve the corresponding stationary Schrödinger equation using the correlated Gaussian method for different particle types, aspect ratios and interactions strength. We show that the idealized model is accurate for small and intermediate strength interactions at aspect ratios larger than four, independently of the particle types. In the strongly interacting limit, the idealized model is acceptable for bosonic systems, but not for fermionic systems even at large aspect ratios.The theoretical study of ultracold few-body systems is often done using an idealized 1D model with zero range interactions. Here we study these systems using a more realistic 3D model with finite range interactions. We place three-particles, two identical and one impurity, in an axial symmetric harmonic trap and solve the corresponding stationary Schrödinger equation using the correlated Gaussian method for different particle types, aspect ratios and interactions strength. We show that the idealized model is accurate for small and intermediate strength interactions at aspect ratios larger than four, independently of the particle types. In the strongly interacting limit, the idealized model is acceptable for bosonic systems, but not for fermionic systems even at large aspect ratios.

arXiv:1910.02705Oct 7, 20190 citations

On the description of fermion systems in boson representations

Bent Sørensen

Nuclear Physics ADec 1, 197332 citations

Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions

Ryota Matsuda, Masahiro Hoshino, Yuto Ashida

Characterizing a quantum state through the lens of quantum resources provides an information-theoretic perspective on many-body systems. While quantum entanglement serves as the paradigmatic example of a quantum resource, recent studies have shown that quantum magic, a resource for universal quantum computation, captures aspects of many-body states complementary to those described by entanglement. For instance, in spin systems, conformal field theory (CFT) analysis of the stabilizer Rényi entropy has revealed universal features of nonstabilizerness qualitatively distinct from entanglement. In bosonic and fermionic systems, however, a comparable formulation for their computational resource, non-Gaussianity, has yet to be established. In this work, we introduce a unified measure, the magic Rényi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing. We show that the MRE is a resource monotone under stabilizer and Gaussian protocols involving measurements and feedforward operations. The MRE reveals common universal aspects of nonstabilizerness and non-Gaussianity in critical many-body states. In particular, our CFT analysis shows that the universal contribution to the MRE appears as the size-independent term determined by the Affleck-Ludwig boundary entropy. We find that non-Gaussianity can continuously renormalize this universal contribution or drive a boundary transition through bulk-induced boundary renormalization-group flows. As a concrete example, we present a CFT analysis of non-Gaussianity in interacting spinless fermions described by the Tomonaga-Luttinger liquid, showing boundary transitions at the Luttinger parameters $K=1/3$ and $K=3$ . Our field-theoretical predictions are confirmed by numerical calculations. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.Characterizing a quantum state through the lens of quantum resources provides an information-theoretic perspective on many-body systems. While quantum entanglement serves as the paradigmatic example of a quantum resource, recent studies have shown that quantum magic, a resource for universal quantum computation, captures aspects of many-body states complementary to those described by entanglement. For instance, in spin systems, conformal field theory (CFT) analysis of the stabilizer Rényi entropy has revealed universal features of nonstabilizerness qualitatively distinct from entanglement. In bosonic and fermionic systems, however, a comparable formulation for their computational resource, non-Gaussianity, has yet to be established. In this work, we introduce a unified measure, the magic Rényi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing. We show that the MRE is a resource monotone under stabilizer and Gaussian protocols involving measurements and feedforward operations. The MRE reveals common universal aspects of nonstabilizerness and non-Gaussianity in critical many-body states. In particular, our CFT analysis shows that the universal contribution to the MRE appears as the size-independent term determined by the Affleck-Ludwig boundary entropy. We find that non-Gaussianity can continuously renormalize this universal contribution or drive a boundary transition through bulk-induced boundary renormalization-group flows. As a concrete example, we present a CFT analysis of non-Gaussianity in interacting spinless fermions described by the Tomonaga-Luttinger liquid, showing boundary transitions at the Luttinger parameters $K=1/3$ and $K=3$. Our field-theoretical predictions are confirmed by numerical calculations. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.

quant-pharXiv:2607.05343Jul 7, 20260 citations

Heat Equation from Exact Renormalization Group Equation (ERGE) at Local Potential Approximation (LPA)

Phumudzo Rabambi

By simply applying the Local Potential Approximation (LPA) on the Polchinski's Exact Renormalization Group (ERG) flow equation for single Bosonic and spinless Fermionic fields, and initially considering only the coarse-graining (blocking) aspect of Wilson's Renormalization Group program. Within the LPA limit the Polchinski's ERG flow equation simplifies into a heat differential equation for both Bosonic and Fermionic fields. Solving the differential equations leads to logarithmic interactions (logarithmic vertex function) in both Bosonic and Fermionic fields at their fixed points.By simply applying the Local Potential Approximation (LPA) on the Polchinski's Exact Renormalization Group (ERG) flow equation for single Bosonic and spinless Fermionic fields, and initially considering only the coarse-graining (blocking) aspect of Wilson's Renormalization Group program. Within the LPA limit the Polchinski's ERG flow equation simplifies into a heat differential equation for both Bosonic and Fermionic fields. Solving the differential equations leads to logarithmic interactions (logarithmic vertex function) in both Bosonic and Fermionic fields at their fixed points.

arXiv:2406.12523Jun 18, 20240 citations

Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

V. K. B. Kota, N. D. Chavda

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

EntropyJul 20, 201811 citations

K=1/3

and

K=3

. Our field-theoretical predictions are confirmed by numerical calculations. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.