EH Lib: Disambiguating Four Scientific Contexts

• EH Lib is a disambiguation term used in multiple fields, including quantum many-body physics, stellar astrophysics, electroweak theory, and collider design.
• In quantum electron models, the EDLib (often misread as EH Lib) employs advanced C++11 templating, MPI/OpenMP parallelization, and innovative matrix storage methods to solve complex Hamiltonians.
• In astrophysics and high-energy studies, EH Lib denotes a high-amplitude δ Scuti star, an EW chiral amplitude toolkit, and an electron–hadron collider synthesis, each defined by distinct methodologies and outcomes.

Searching arXiv for the cited topics to ground the article in the relevant papers. Search query: arXiv papers matching "Exact Diagonalization library for quantum electron models" and "EDLib" “EH Lib” is not a single standardized scientific object in the materials considered here. Instead, it designates four different referents: EDLib, often misread as “EH Lib,” a C++ exact diagonalization library for quantum electron models; EH Librae, a high-amplitude $\delta$ Scuti star; a tutorial-style “EH Library” description of software tools for computing electroweak chiral amplitudes; and an “EH Lib” entry synthesizing the Large Hadron–Electron Collider concept at the LHC (Iskakov et al., 2017, Xie et al., 20 Jul 2025, Martinez-Martin et al., 2022, André et al., 2022). In practice, the meaning of the term is therefore entirely context-dependent.

1. Referential scope

In the sources represented here, the label appears in four distinct research contexts (Iskakov et al., 2017, Xie et al., 20 Jul 2025, Martinez-Martin et al., 2022, André et al., 2022).

Referent in the materials	Domain	Core description
EDLib, often misread as “EH Lib”	Correlated-electron computation	C++11 template library for exact diagonalization
EH Librae	Stellar astrophysics	High-amplitude $\delta$ Scuti star
“EH Library” for EW amplitudes	High-energy theory software	EWET/HEFT implementation in Mathematica packages
“EH Lib” for LHeC	Electron–hadron collider physics	Synthesis of the LHeC concept

The first usage is the most literal software-library sense. EDLib is described as an exact diagonalization C++ template library for solving quantum electron models, including single-band finite Hubbard clusters and multi-orbital impurity Anderson models. The second is an astronomical abbreviation: EH Lib is the star EH Librae. The third uses “EH Library” as a convenient label for a software stack implementing the Electroweak Chiral Lagrangian in FeynRules, FeynArts, and FeynCalc. The fourth uses “EH Lib” as an entry title for electron–hadron scattering at the LHC, specifically the LHeC concept.

This suggests that “EH Lib” is best treated as a disambiguation problem rather than a unified technical term.

2. EDLib: exact diagonalization for quantum electron models

EDLib is a C++11 template library designed to perform exact diagonalization of quantum electron Hamiltonians, with a focus on finite Hubbard clusters and multi-orbital Anderson impurity models (Iskakov et al., 2017). It is parallelized using MPI and OpenMP, built on top of ALPSCore and ARPACK-NG, and intended as a research tool, a benchmarking platform, and an educational framework.

The supported single-band finite Hubbard model is written as

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$

with

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$

and

$$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$

The multi-orbital impurity Anderson model is given in the source by

$$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$

In both cases, EDLib exploits conservation of $N_\uparrow$ and $N_\downarrow$ to block-diagonalize the Hamiltonian. In the occupation-number basis, the full Hilbert-space dimension is

$M = 2^{2N_s},$

while a fixed sector has dimension

$$M_{N_\uparrow,N_\downarrow} = \binom{N_s}{N_\uparrow} \binom{N_s}{N_\downarrow}.$$

The library uses bit representations internally to encode occupation patterns and relies on Lanczos and ARPACK-NG Krylov methods for low-lying eigenspectra and Green’s functions.

A central architectural feature is the choice among three Hamiltonian storage strategies. The spin-resolved format uses

$\delta$0

so that two smaller matrices are stored instead of the full matrix. The custom Signs-Only Compressed Row Storage stores only the fermionic signs of off-diagonal hopping terms in compressed bitwise form, with hopping magnitudes retrieved from the adjacency matrix. Conventional sparse or dense storage is also available for smaller systems. The library computes single-particle Green’s functions, spin–spin correlation functions, eigenvalues, eigenvectors, and ground-state properties. Its demonstrated applications include a 16-site Hubbard cluster and a multi-orbital Co/Pt(111) Anderson impurity calculation with a largest sector of approximately $\delta$1 basis states.

In this usage, “EH Lib” is not the official name; the source explicitly states that EDLib is often misread as “EH Lib.” That distinction is important, because the underlying software identity is EDLib.

3. EH Librae: a high-amplitude $\delta$2 Scuti star

In stellar astrophysics, EH Lib denotes EH Librae, a high-amplitude $\delta$3 Scuti star characterized in combined ground-based and TESS data (Xie et al., 20 Jul 2025). The study identifies it as a single-mode HADS star whose pulsation is dominated by the fundamental radial mode, with two additional very low-amplitude frequencies.

The dominant frequency is

$\delta$4

with period

$\delta$5

The TESS analysis reports harmonics up to $\delta$6, together with

$\delta$7

The pulsation constant is derived as

$\delta$8

consistent with the interpretation of $\delta$9 as the fundamental radial mode. The period–luminosity relation and the Gaia DR3 parallax are also used to support that identification.

A central result is the secular period increase obtained from an $$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$0 diagram constructed from 342 times of maximum light spanning about 70 years:

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$1

The quadratic ephemeris term is reported as non-zero at the $$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$2 level, and the authors interpret the positive period change as evolutionary rather than binary in origin. Their MESA and GYRE modelling, constrained by both $$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$3 and $$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$4, yields

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$5

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$6

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$7

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$8

and

$$\mathcal{H} = \mathcal{H}_{loc} + \mathcal{H}_{hop},$$9

The star is located in the Hertzsprung gap, with a helium core and a hydrogen-burning shell, and is described as an AE UMa analogue because both stars have similar fundamental frequencies, similar period change rates, subsolar metallicity, and post-main-sequence status. The contrast is that AE UMa is double-mode whereas EH Lib is single-mode.

Here the abbreviation is astronomical and conventional: “EH Lib” is simply the shortened designation of EH Librae.

4. “EH Library” for electroweak chiral amplitudes

A different usage appears in high-energy theory software, where the phrase “EH Library” is used as a tutorial-style label for software tools implementing the Electroweak Chiral Lagrangian, also denoted as HEFT or EWET, in Mathematica-based packages (Martinez-Martin et al., 2022). The work implements the bosonic part of the electroweak Lagrangian up to next-to-leading order for FeynRules, FeynArts, and FeynCalc.

The underlying effective theory has the custodial symmetry-breaking pattern

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$0

with Goldstones collected in

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$1

The gauge matrices are

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$2

and the covariant derivative is

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$3

The Lagrangian is organized in chiral dimension,

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$4

with the bosonic sector implemented up to $$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$5.

At leading order, the source gives the field-strength and scalar parts as

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$6

and

$$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$7

The NLO implementation includes CP-even and CP-odd bosonic operators with Higgs-dependent coefficient functions $$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$8 and $$\mathcal{H}_{loc} = \sum_i U_i\, n_{i\uparrow} n_{i\downarrow} - \sum_{i\sigma} \mu_i\, n_{i\sigma},$$9, represented in code by names such as F1n2 and FF1n2.

The software stack consists of the FeynRules model file EWET.fr, the notebook EWET FeynRules.nb, and pre-generated FeynArts model files such as SixPartVertsLagr.mod, SixPartVertsLagr.gen, and SixPartVertsLagr.pars, together with EWET FeynCalc.nb. Vertices are generated up to six external fields by expanding a dummy variable epsf up to epsf^6. The implementation allows automatic generation of tree-level amplitudes with arbitrary operator insertions and one-loop amplitudes using only $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$0 vertices up to four external legs. A worked example is $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$1, for which the source reports 179 one-loop diagrams when $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$2 vertices are allowed generally, and 22 diagrams at strict $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$3.

The SM appears as a specific limit obtained by setting the non-SM NLO coefficients to zero and choosing SM-like values such as $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$4 and $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$5. The stated limitations are equally important: only the bosonic sector is implemented; ghosts, fermions, and gluons are postponed; gauge fixing and renormalization are not fully automated.

5. “EH Lib” in electron–hadron scattering: the LHeC synthesis

The designation also appears as an “EH Lib” entry for electron–hadron scattering at the LHC, centered on the Large Hadron–Electron Collider proposal (André et al., 2022). The concept is a future, luminous, energy-frontier $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$6 scattering experiment at the LHC, designed to complement the HL-LHC proton–proton and heavy-ion program.

The proposal considers an electron beam with $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$7, with a possible later upgrade to $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$8, colliding with $$\mathcal{H}_{hop} = \sum_{\langle i,j\rangle,\sigma} t_{ij}\, c^{\dagger}_{i\sigma} c_{j\sigma}.$$9 protons. The source gives

$$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$0

and states $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$1 for $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$2 and $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$3 in its overview, while a later kinematic estimate writes $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$4 from the same relation. The target luminosity is around $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$5, with integrated luminosity goals up to $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$6, and an initial $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$7 is described as already transformative for PDFs.

The physics program is broad. In DIS, it aims at determination of all PDFs $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$8 and $$\begin{aligned} H = &\sum_{p\sigma} \epsilon_p\, c^{\dagger}_{p\sigma} c_{p\sigma} + \sum_{i\sigma} (\epsilon_i - \mu)\, n_{i\sigma} + \sum_{ip\sigma} \bigl( V_{ip}\, d^{\dagger}_{i\sigma} c_{p\sigma} + \text{H.c.} \bigr) \ &+ \frac{1}{2} \sum_{ijkl,\sigma\sigma'} U_{ijkl}\, d^{\dagger}_{i\sigma} d^{\dagger}_{j\sigma'} d_{l\sigma'} d_{k\sigma}. \end{aligned}$$9 in a single experiment over many orders of magnitude in $N_\uparrow$0 and $N_\uparrow$1, precision extraction of $N_\uparrow$2, direct measurement of $N_\uparrow$3, heavy-flavor PDFs, and resolution of small-$N_\uparrow$4 dynamics. For Higgs physics, the dominant production mechanism is charged-current $N_\uparrow$5 fusion,

$N_\uparrow$6

with an inclusive CC Higgs cross section of about $N_\uparrow$7 at the LHeC. The program also includes top-quark physics, electroweak precision tests, and a wide BSM portfolio, including sterile neutrinos, heavy scalars, lepton flavor violation, seesaw scenarios, leptoquarks, and dark photons.

The detector concept is a general-purpose $N_\uparrow$8 detector with a silicon tracker, liquid-argon electromagnetic calorimetry, steel-and-scintillator hadronic calorimetry, muon chambers, and very forward/backward taggers. Coverage extends to approximately $N_\uparrow$9, and the tracker is designed for $N_\downarrow$0 impact parameter resolution. The accelerator concept uses a multi-turn energy-recovery linac with two superconducting linacs of about $N_\downarrow$1 each, three return arcs on each side, a beam energy of $N_\downarrow$2, bunch charge $N_\downarrow$3, bunch spacing $N_\downarrow$4, current $N_\downarrow$5, RF frequency $N_\downarrow$6, gradient $N_\downarrow$7, and total ERL length $N_\downarrow$8.

A distinctive feature is the possibility of a common interaction region that alternately could serve $N_\downarrow$9 and $M = 2^{2N_s},$0 collisions while other experiments remain on $M = 2^{2N_s},$1. The text also sketches a forward–backward symmetrised detector option, extending the program toward hadron–hadron and heavy-ion physics.

6. Comparative interpretation

Across these sources, the designation “EH Lib” spans exact diagonalization for correlated electrons, asteroseismology of a high-amplitude $M = 2^{2N_s},$2 Scuti star, electroweak EFT software, and electron–hadron collider design (Iskakov et al., 2017, Xie et al., 20 Jul 2025, Martinez-Martin et al., 2022, André et al., 2022). The underlying objects are methodologically and scientifically unrelated.

A common misconception would be to treat “EH Lib” as the name of a single library or package. In one source it is explicitly a misreading of EDLib; in another it is a stellar abbreviation; in a third it is a convenient label for an EWET/HEFT toolchain; and in a fourth it denotes an electron–hadron knowledge-base style synthesis of the LHeC concept. This suggests that the term has no stable meaning outside its immediate disciplinary context.

For practical use, context is decisive. In correlated-electron many-body physics, “EH Lib” most plausibly points to EDLib. In variable-star work, it refers to EH Librae. In high-energy phenomenology software, it can denote an EW chiral amplitude toolkit. In collider design discussions, it can denote electron–hadron physics centered on the LHeC. The same character string therefore maps onto different epistemic objects: a numerical solver, a pulsating star, an EFT implementation, or a collider program.