We consider bulk-gapped fermion systems whose infinite-volume bulk is obtained by adding sufficiently weak even many-body interactions to a free Hamiltonian with spectral gap $g>0$ , allowing polynomial spatial decay of both parts. We prove quantitative local determination of low-energy states: whenever another interaction agrees with the bulk interaction inside a finite or infinite region $U$ , with bulk terms crossing its boundary unchanged or removed, all its states with excitation energies in $[0,3g/4]$ have local expectations close to those of the bulk ground state deep inside $U$ . The error decays with the distance to the complement of $U$ , independently of the interaction terms supported outside $U$ and of the chosen low-energy state. Quantitative local determination has strong consequences. (i) The bulk interaction has a unique algebraic ground state. (ii) A strong "local perturbations perturb locally" (LPPL) principle holds: arbitrary distant defects change local ground-state expectations only by a spatially decaying error. (iii) Low-energy excitations in finite samples remain localized near the boundary for all times, up to spatially decaying tails, uniformly over arbitrary even boundary terms. (iv) Correlations from deep inside $U$ to outside $U$ are small, with quantitative bounds in terms of spatial separation and distance to $U^c$ . To prove local determination of low-energy states, we combine quasi-adiabatic transport of the free ground state to the interacting bulk ground state with a new condition, local excitation detectability (LED). A companion paper establishes gap stability and constructs the transport for weak interactions, while we prove LED at sufficiently weak coupling. The abstract theorem is nonperturbative and applies whenever the transport and LED hypotheses hold.We consider bulk-gapped fermion systems whose infinite-volume bulk is obtained by adding sufficiently weak even many-body interactions to a free Hamiltonian with spectral gap $g>0$, allowing polynomial spatial decay of both parts. We prove quantitative local determination of low-energy states: whenever another interaction agrees with the bulk interaction inside a finite or infinite region $U$, with bulk terms crossing its boundary unchanged or removed, all its states with excitation energies in $[0,3g/4]$ have local expectations close to those of the bulk ground state deep inside $U$. The error decays with the distance to the complement of $U$, independently of the interaction terms supported outside $U$ and of the chosen low-energy state. Quantitative local determination has strong consequences. (i) The bulk interaction has a unique algebraic ground state. (ii) A strong "local perturbations perturb locally" (LPPL) principle holds: arbitrary distant defects change local ground-state expectations only by a spatially decaying error. (iii) Low-energy excitations in finite samples remain localized near the boundary for all times, up to spatially decaying tails, uniformly over arbitrary even boundary terms. (iv) Correlations from deep inside $U$ to outside $U$ are small, with quantitative bounds in terms of spatial separation and distance to $U^c$. To prove local determination of low-energy states, we combine quasi-adiabatic transport of the free ground state to the interacting bulk ground state with a new condition, local excitation detectability (LED). A companion paper establishes gap stability and constructs the transport for weak interactions, while we prove LED at sufficiently weak coupling. The abstract theorem is nonperturbative and applies whenever the transport and LED hypotheses hold.

math-phCross-listedarXiv:2610.40337Oct 30, 20260 citations

An exact calculation of the free energy in systems with separable interactions. II

P.A.J. Tindemans, Hans W. Capel

PhysicaAug 1, 197447 citations

Systems with separable many-particle interactions. II

L.W.J. den Ouden, Hans W. Capel, Jacques H. H. Perk

Physica A Statistical Mechanics and its ApplicationsJan 1, 197641 citations

Space-Time Method forAb InitioCalculations of Self-Energies and Dielectric Response Functions of Solids

H. Rojas, Rex W. Godby, Richard J. Needs

We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real-space/imaginary-time representation, (ii) avoidance of any model form for the screened interaction $W$ , (iii) exact separation of $W$ and the self-energy $\ensuremath{\Sigma}$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real-space/imaginary-time representation, (ii) avoidance of any model form for the screened interaction $W$, (iii) exact separation of $W$ and the self-energy $\ensuremath{\Sigma}$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.

Physical Review LettersMar 6, 1995266 citations

Systems with separable many-particle interactions. I

L.W.J. den Ouden, Hans W. Capel, Jacques H. H. Perk +1 more

Physica A Statistical Mechanics and its ApplicationsJan 1, 197628 citations

We consider bulk-gapped fermion systems whose infinite-volume bulk is obtained by adding sufficiently weak even many-body interactions to a free Hamiltonian with spectral gap

g>0

, allowing polynomial spatial decay of both parts. We prove quantitative local determination of low-energy states: whenever another interaction agrees with the bulk interaction inside a finite or infinite region

U

, with bulk terms crossing its boundary unchanged or removed, all its states with excitation energies in

[0,3g/4]

have local expectations close to those of the bulk ground state deep inside

U

. The error decays with the distance to the complement of

U

, independently of the interaction terms supported outside

U

and of the chosen low-energy state. Quantitative local determination has strong consequences. (i) The bulk interaction has a unique algebraic ground state. (ii) A strong "local perturbations perturb locally" (LPPL) principle holds: arbitrary distant defects change local ground-state expectations only by a spatially decaying error. (iii) Low-energy excitations in finite samples remain localized near the boundary for all times, up to spatially decaying tails, uniformly over arbitrary even boundary terms. (iv) Correlations from deep inside

U

to outside

U

are small, with quantitative bounds in terms of spatial separation and distance to

U^c

. To prove local determination of low-energy states, we combine quasi-adiabatic transport of the free ground state to the interacting bulk ground state with a new condition, local excitation detectability (LED). A companion paper establishes gap stability and constructs the transport for weak interactions, while we prove LED at sufficiently weak coupling. The abstract theorem is nonperturbative and applies whenever the transport and LED hypotheses hold.

W

, (iii) exact separation of

W

and the self-energy $\ensuremath{\Sigma}$ into short- and long-ranged parts, and (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.