many_body_certification

This header-based C++ library implements semidefinite-programming relaxations for quantum spin systems. It computes lower bounds on ground-state energies and upper and lower bounds on observables. The implementation supports translation, sign, and lattice symmetries and is used by the model drivers in the sibling steady_state_phase_transitions repository.

The code was used for Mapping phase diagrams of quantum spin systems through semidefinite-programming relaxations.

Installation

See INSTALL.md for complete macOS and Linux setup instructions. It covers the compiler and library requirements, MOSEK license setup, all required environment variables, verification commands, and integration with steady_state_phase_transitions.

The short version, after installing the dependencies, is:

export CXX=clang++
export MOSEK=/path/to/mosek/platform-directory
export EIGEN=/path/to/include/eigen3
export XTENSOR=/path/to/include
export XTL=/path/to/include

make -C cpp test_normal_form_fast
./cpp/bin/test_normal_form_fast

Do not edit machine-local dependency paths into the Makefile. Set them in the shell or in a local shell startup file instead.

Repository layout

• cpp/include/: reusable lattice, operator, Hamiltonian, RDM, and SDP headers
• cpp/include/sos/: sum-of-squares and momentum-sector SDP routines
• cpp/src/: model programs
• cpp/tests/: focused examples and tests
• cpp/bin/: locally built executables (generated artifacts)

Building

Build from this repository's cpp directory through its Makefile. For example, the portable normal-form test is:

make -C cpp test_normal_form_fast
./cpp/bin/test_normal_form_fast

Targets are built independently and executables are written to cpp/bin/. There is no default all target. The test and example sources are the most reliable reference for constructing new models; start with cpp/tests/simple_spin_chain.cpp for a small spin-system example. Some older targets use platform-specific linker flags; INSTALL.md gives the appropriate MOSEK-linked smoke target for macOS and Linux.

Cleaning

make -C cpp clean

This removes every file under cpp/bin/, so copy any executable you need to keep before running it.