merapp

Official Resources

• Repository: https://github.com/g1257/merapp
• License: GNU General Public License v3.0
• Developer: Gonzalo Alvarez (g1257)

Overview

merapp (MERA++) is a robust C++ implementation of the Multi-scale Entanglement Renormalization Ansatz (MERA) algorithm. It is part of a suite of tools (including DMRG++) designed for the simulation of strongly correlated quantum systems. MERA++ is specifically engineered to handle scale-invariant systems and quantum critical points by optimizing the MERA tensor network, which adds an extra dimension of "scale" to efficiently capture critical entanglement.

Scientific domain: Quantum Critical Phenomena, Conformal Field Theory (CFT), Condensed Matter. Target user community: Physicists studying quantum phase transitions and critical points.

Theoretical Methods

• MERA: Ternary, Binary, and Modified Binary MERA ansatzes.
• Entanglement Renormalization: Using isometries and disentanglers to coarse-grain the lattice.
• Variational Optimization: Minimizing energy expectation value.
• Scale Invariance: Determining scaling dimensions and central charge.

Capabilities (CRITICAL)

• Generic Engine: Supports arbitrary dimensions, arities, and geometries.
• Hamiltonians: Built-in support for Heisenberg, Hubbard, t-J, and other models.
• Symmetries: U(1), Z2, and SU(2) symmetry support via PsimagLite backend.
• Observables: Computation of energy, correlation functions, and scaling operators.
• Parallelism: Shared memory parallelization (pthreads/OpenMP).

Key Strengths

Specialization

• One of the few open-source, production-ready codes specifically for MERA.
• Handles the complex geometry of MERA networks efficiently.

Performance

• Written in optimized C++.
• Exploits symmetries to drastically reduce tensor sizes.

Inputs & Outputs

• Input: Input file defining model parameters, MERA type, and symmetry sector.
• Output: Ground state energy, Optimized tensors, Conformal data (scaling dims).

Interfaces & Ecosystem

• Dependencies: PsimagLite (linear algebra/utils library from same author).
• Interface: Command-line driven.
• Ecosystem: Compatible with DMRG++ input formats and utilities.

Advanced Features

• Conformal Data: Extraction of central charge and primary field scaling dimensions.
• Restart: Continuation of optimization from saved states.

Performance Characteristics

• Cost: MERA contraction is $O(\chi^7)$ or similar, making it expensive but polynomial.
• Optimization: Uses efficient local update strategies.

Computational Cost

• High: Significantly more expensive than DMRG for the same bond dimension, but captures criticality better.

Comparison with Other Codes

• vs DMRG: DMRG (MPS) fails to capture critical entanglement (logarithmic growth) efficiently; MERA succeeds but at higher constant cost.
• vs TeNPy: TeNPy focuses on MPS; MERA++ focuses on MERA.

Application Areas

• Quantum Critical Points: Ising, Potts, Heisenberg transitions.
• Topological Phases: Study of topological order using MERA.

Best Practices

• Symmetries: Use symmetries whenever possible to enable larger $\chi$.
• Convergence: Monitor energy and scaling dimensions for stability.

Verification & Sources

Primary sources:

1. Repository: https://github.com/g1257/merapp
2. Associated papers by G. Alvarez on MERA/DMRG.

Confidence: VERIFIED - Open source distribution. Verification status: ✅ VERIFIED