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Quantum Studies Mathematics and Foundations

Can quantum Rabi model with $${\varvec{A}}^\textbf{2}$$-term avoid no-go theorem and make quantum simulation of mass-enhancement in SUSY breaking?

Masao Hirokawa

Published Jul 1, 2024• 0 citations
Publisher

Abstract

Abstract We study the model of a mass enhancement in the supersymmetric quantum mechanics. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. It is evolved from a prototype based on the quantum Rabi model. Here, our quantum simulation means the realization of the target quantum phenomenon as a physical entity with some quantum-information devices. The original prototype is given as a mathematical model, and has the transition from the $${\mathcal {N}}=2$$ N = 2 SUSY to its spontaneous breaking, though it has no mass enhancement. It is recently reported that the transition is observed for this prototype in a trapped-ion experiment with devising a method experimentally to realize the transition. The model proposed in this paper describes how the mass enhancement takes place in the fermionic states by the excitation of the 1-mode light boson in the SUSY breaking. In this model, the bosonic and fermionic states are graded by qubits. Although our model’s interaction does not have the Higgs potential, the mass enhancement in the fermionic states is caused by the radiative enhancement with the help of the X-gate’s swap between the fermionic and bosonic states.

DOI
10.1007/s40509-024-00342-7

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Abstract We study the model of a mass enhancement in the supersymmetric quantum mechanics. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. It is evolved from a prototype based on the quantum Rabi model. Here, our quantum simulation means the realization of the target quantum phenomenon as a physical entity with some quantum-information devices. The original prototype is given as a mathematical model, and has the transition from the N=2{\mathcal {N}}=2N=2 N = 2 SUSY to its spontaneous breaking, though it has no mass enhancement. It is recently reported that the transition is observed for this prototype in a trapped-ion experiment with devising a method experimentally to realize the transition. The model proposed in this paper describes how the mass enhancement takes place in the fermionic states by the excitation of the 1-mode light boson in the SUSY breaking. In this model, the bosonic and fermionic states are graded by qubits. Although our model’s interaction does not have the Higgs potential, the mass enhancement in the fermionic states is caused by the radiative enhancement with the help of the X-gate’s swap between the fermionic and bosonic states.
We study a quantum-simulation model of a mass enhancement in the fermionic states, as well as in the bosonic ones, of the supersymmetric quantum mechanics. The bosonic and fermionic states are graded by a qubit. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. Here, our quantum simulation means the realization of the target quantum phenomenon with some quantum-information devices as a physical reality. The model describes how the quasi-particle consisting of the annihilation and creation of 1-mode scalar bosons eats the spin effect given by the X-gate, and how it acquires the mass enhancement in the fermionic states in the spontaneous SUSY breaking. Our model's interaction does not have any Higgs potential. Instead, the qubit acts as a substitute for the Higgs potential by the 2-level-system approximation of the double-well potential, and then, the spontaneous SUSY breaking takes place and the mass is enhanced.
Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system.
The renormalized quantum Rabi model describing a qubit-boson interaction has the transition from SUSY to its spontaneous breaking under suitable conditions. It is caused by how the X-gate coupled to the Bose field works properly between the two symmetrical wells made by the bosons coupled to a qubit. According to Polyakov's idea, there is the possibility that an instanton tunneling the barrier between those symmetrical wells appears as the classical trajectory. In this paper, therefore, under a physical condition, we show the vestige of the particle like an instanton in the expression of the ground-state energy of the quantum Rabi model.
We study a model of interacting spinless fermions in a one dimensional lattice with supersymmetry (SUSY). The Hamiltonian is given by the anticommutator of two supercharges QQQ and ${Q}^{\ifmmode\dagger\else\textdagger\fi{}}$, each of which is comprised solely of fermion operators and possesses one adjustable parameter ggg. When the parameter ggg vanishes, the model is identical to the one studied by Nicolai [H. Nicolai, J. Phys. A 9, 1497 (1976)], where the zero-energy ground state is exponentially degenerate. On the other hand, in the large-ggg limit the model reduces to the free-fermion chain with a four-fold degenerate ground state. We show that for finite chains SUSY is spontaneously broken when g>0g>0g>0. We also rigorously prove that for sufficiently large ggg the ground-state energy density is nonvanishing in the infinite-volume limit. We further analyze the nature of the low-energy excitations by employing various techniques such as rigorous inequalities, exact numerical diagonalization, and renormalization group method with bosonization. The analysis reveals that the low-energy excitations are described by massless Dirac fermions (or Thirring fermions more generally), which can be thought of as Nambu-Goldstone fermions from the spontaneous SUSY breaking.
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle physics and fostering connections to theories of quantum gravity. However, lattice studies exploring the non-perturbative features of these models, such as spontaneous supersymmetry breaking and real-time evolution encounter significant challenges, particularly due to the infamous sign problem. The sign problem obstructs simulations on classical computers, especially when dealing with high-dimensional lattice systems. While one potential solution is to adopt the Hamiltonian formalism, this approach necessitates an exponential increase in classical resources with the number of lattice sites and degrees of freedom, rendering it impractical for large systems. In contrast, quantum hardware offers a promising alternative, as it requires in principle a polynomial amount of resources, making the study of these models more accessible. In this context, we explore the encoding of lower-dimensional supersymmetric quantum mechanics onto qubits. We also highlight our ongoing efforts to implement and check the model supersymmetry breaking on an IBM gate-based quantum simulator with and without shot noise, addressing the technical challenges we face and the potential implications of our findings for advancing our understanding of supersymmetry.
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle physics and fostering connections to theories of quantum gravity. However, lattice studies exploring the non-perturbative features of these models, such as spontaneous supersymmetry breaking and real-time evolution encounter significant challenges, particularly due to the infamous sign problem. The sign problem obstructs simulations on classical computers, especially when dealing with high-dimensional lattice systems. While one potential solution is to adopt the Hamiltonian formalism, this approach necessitates an exponential increase in classical resources with the number of lattice sites and degrees of freedom, rendering it impractical for large systems. In contrast, quantum hardware offers a promising alternative, as it requires in principle a polynomial amount of resources, making the study of these models more accessible. In this context, we explore the encoding of lower-dimensional supersymmetric quantum mechanics onto qubits. We also highlight our ongoing efforts to implement and check the model supersymmetry breaking on an IBM gate-based quantum simulator with and without shot noise, addressing the technical challenges we face and the potential implications of our findings for advancing our understanding of supersymmetry.